Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
19201	Find the Exact Value	1/(cot(234))	$\frac{1}{\cot (234)}$
19202	Find the Exact Value	1/(sin(60))	$\frac{1}{\sin (60)}$
19203	Find the Exact Value	1/(-sin(60))	$\frac{1}{- \sin (60)}$
19204	Find the Exact Value	1/(cot(49.6))	$\frac{1}{\cot (49.6)}$
19205	Find the Exact Value	-1/(2sin(0))	$- \frac{1}{2 \sin (0)}$
19206	Find the Exact Value	0.8/(cos(70))	$\frac{0.8}{\cos (70)}$
19207	Find the Exact Value	(480sin(44))/780	$\frac{480 \sin (44)}{780}$
19208	Find the Exact Value	1/(cos(90))	$\frac{1}{\cos (90)}$
19209	Find the Exact Value	(sin(32)*20)/(sin(34))	$\frac{\sin (32) \cdot 20}{\sin (34)}$
19210	Find the Exact Value	(sin(34)*60)/(sin(75))	$\frac{\sin (34) \cdot 60}{\sin (75)}$
19211	Find the Exact Value	(96sin(80)sin(65)*sin(35))/(sin(20)+sin(50)+sin(110))	$\frac{96 \cdot \sin (80) \cdot \sin (65) \cdot \sin (35)}{\sin (20) + \sin (50) + \sin (110)}$
19212	Find the Exact Value	(sin(60))(cos(60))	$(\sin (60)) (\cos (60))$
19213	Find the Exact Value	cos(45)^2-sin(45)^2	$\cos^{2} (45) - \sin^{2} (45)$
19214	Find the Exact Value	(6/(tan(15))*144)/2	$\frac{\frac{6}{\tan (15)} \cdot 144}{2}$
19215	Find the Exact Value	(sin(45)^2)/(cos(45)^2)	$\frac{\sin^{2} (45)}{\cos^{2} (45)}$
19216	Find the Exact Value	1/(cos(pi/4)^2)	$\frac{1}{\cos^{2} (\frac{π}{4})}$
19217	Verify the Identity	sin(x)^2sec(x)csc(x)=tan(x)	$\sin^{2} (x) \sec (x) \csc (x) = \tan (x)$
19218	Verify the Identity	(sin(x+h)-sin(x))/h=cos(x)((sin(h))/h)-sin(x)(1-cos(h))/h	$\frac{\sin (x + h) - \sin (x)}{h} = \cos (x) (\frac{\sin (h)}{h}) - \sin (x) \frac{1 - \cos (h)}{h}$
19219	Verify the Identity	(sin(x+y)+sin(x-y))/(cos(x+y)+cos(x-y))=tan(x)	$\frac{\sin (x + y) + \sin (x - y)}{\cos (x + y) + \cos (x - y)} = \tan (x)$
19220	Verify the Identity	(sin(x+y)+sin(x-y))/(cos(x+y)+cos(x-y))=tan(y)	$\frac{\sin (x + y) + \sin (x - y)}{\cos (x + y) + \cos (x - y)} = \tan (y)$
19221	Verify the Identity	(sin(x)cos(y)-cos(x)sin(y))/(cos(x)cos(y)+sin(x)sin(y))=(tan(x)-tan(y))/(1+tan(x)tan(y))	$\frac{\sin (x) \cos (y) - \cos (x) \sin (y)}{\cos (x) \cos (y) + \sin (x) \sin (y)} = \frac{\tan (x) - \tan (y)}{1 + \tan (x) \tan (y)}$
19222	Verify the Identity	sin(x)^2-cos(x)^2=1-2cos(x)^2	$\sin^{2} (x) - \cos^{2} (x) = 1 - 2 \cos^{2} (x)$
19223	Verify the Identity	(sin(x+y))/(sin(x-y))=(tan(x)+tan(y))/(tan(x)-tan(y))	$\frac{\sin (x + y)}{\sin (x - y)} = \frac{\tan (x) + \tan (y)}{\tan (x) - \tan (y)}$
19224	Verify the Identity	sin(x)^2cos(x)^2=1/8*(1-cos(4x))	$\sin^{2} (x) \cos^{2} (x) = \frac{1}{8} \cdot (1 - \cos (4 x))$
19225	Verify the Identity	(sin(x-y))/(sin(x)cos(y))=1-cot(x)tan(y)	$\frac{\sin (x - y)}{\sin (x) \cos (y)} = 1 - \cot (x) \tan (y)$
19226	Verify the Identity	(sin(x-y))/(sin(x+y))=(tan(x)-tan(y))/(tan(x)+tan(y))	$\frac{\sin (x - y)}{\sin (x + y)} = \frac{\tan (x) - \tan (y)}{\tan (x) + \tan (y)}$
19227	Verify the Identity	(sin(x))/(cos(x))+(cos(x))/(sin(x))=csc(x)sec(x)	$\frac{\sin (x)}{\cos (x)} + \frac{\cos (x)}{\sin (x)} = \csc (x) \sec (x)$
19228	Verify the Identity	(sin(x)+cos(x))/(sin(x)cos(x))=sec(x)+csc(x)	$\frac{\sin (x) + \cos (x)}{\sin (x) \cos (x)} = \sec (x) + \csc (x)$
19229	Verify the Identity	(sin(x)+sin(3x)+sin(5x))/(cos(x)+cos(3x)+cos(5x))=tan(3x)	$\frac{\sin (x) + \sin (3 x) + \sin (5 x)}{\cos (x) + \cos (3 x) + \cos (5 x)} = \tan (3 x)$
19230	Verify the Identity	(sin(x)+tan(x))/(1+cos(x))=tan(x)	$\frac{\sin (x) + \tan (x)}{1 + \cos (x)} = \tan (x)$
19231	Verify the Identity	(tan(2x)-tan(7x))/(1+tan(2x)tan(7x))=1	$\frac{\tan (2 x) - \tan (7 x)}{1 + \tan (2 x) \tan (7 x)} = 1$
19232	Verify the Identity	(tan(4x))/(tan(x))=4	$\frac{\tan (4 x)}{\tan (x)} = 4$
19233	Verify the Identity	(tan(a)-tan(b))/(cot(b)-cot(a))=(tan(b))/(cot(a))	$\frac{\tan (a) - \tan (b)}{\cot (b) - \cot (a)} = \frac{\tan (b)}{\cot (a)}$
19234	Verify the Identity	(tan(t)-cot(t))/(sin(t)cos(t))=sec(t)^2-csc(t)^2	$\frac{\tan (t) - \cot (t)}{\sin (t) \cos (t)} = \sec^{2} (t) - \csc^{2} (t)$
19235	Verify the Identity	(tan(u-1))/(tan(u+1))=(1-cot(u))/(1+cot(u))	$\frac{\tan (u - 1)}{\tan (u + 1)} = \frac{1 - \cot (u)}{1 + \cot (u)}$
19236	Verify the Identity	sin(x)^4+cos(x)^4=1-2sin(x)^2cos(x)^2	$\sin^{4} (x) + \cos^{4} (x) = 1 - 2 \sin^{2} (x) \cos^{2} (x)$
19237	Verify the Identity	(tan(x))/(sin(x))=sec(x)	$\frac{\tan (x)}{\sin (x)} = \sec (x)$
19238	Verify the Identity	tan(x)^2-2sec(x)^2=-3	$\tan^{2} (x) - 2 \sec^{2} (x) = - 3$
19239	Verify the Identity	(tan(x))/(csc(x))=sec(x)-cos(x)	$\frac{\tan (x)}{\csc (x)} = \sec (x) - \cos (x)$
19240	Verify the Identity	sin(x)^2+1=2-cos(x)^2	$\sin^{2} (x) + 1 = 2 - \cos^{2} (x)$
19241	Verify the Identity	sin(x)^2=1/2*(1-cos(2x))	$\sin^{2} (x) = \frac{1}{2} \cdot (1 - \cos (2 x))$
19242	Verify the Identity	sin(x)^2cos(x)^2=(1-cos(4x))/8	$\sin^{2} (x) \cos^{2} (x) = \frac{1 - \cos (4 x)}{8}$
19243	Verify the Identity	sin(x)^3cos(x)^4=(cos(x)^4-cos(x)^6)sin(x)	$\sin^{3} (x) \cos^{4} (x) = (\cos^{4} (x) - \cos^{6} (x)) \sin (x)$
19244	Verify the Identity	sin(x)^2=2+2cos(x)	$\sin^{2} (x) = 2 + 2 \cos (x)$
19245	Verify the Identity	sin(5x)^4+cos(5x)^4+2sin(5x)^2cos(5x)^2=1	$\sin^{4} (5 x) + \cos^{4} (5 x) + 2 \sin^{2} (5 x) \cos^{2} (5 x) = 1$
19246	Verify the Identity	sin(x)^4=1/4*(1-cos(4x))	$\sin^{4} (x) = \frac{1}{4} \cdot (1 - \cos (4 x))$
19247	Verify the Identity	sin(x)^6+cos(x)^6=1-3sin(x)^2cos(x)^2	$\sin^{6} (x) + \cos^{6} (x) = 1 - 3 \sin^{2} (x) \cos^{2} (x)$
19248	Verify the Identity	1-2sin(x)^2cos(x)^2-2sin(x)^4=cos(2x)	$1 - 2 \sin^{2} (x) \cos^{2} (x) - 2 \sin^{4} (x) = \cos (2 x)$
19249	Verify the Identity	1-2sin(a)^2=cos(a)^2-sin(a)^2	$1 - 2 \sin^{2} (a) = \cos^{2} (a) - \sin^{2} (a)$
19250	Verify the Identity	1+cos(2x)-cos(x)^2=cos(x)^2	$1 + \cos (2 x) - \cos^{2} (x) = \cos^{2} (x)$
19251	Verify the Identity	1+cos(12x)=2cos(12x)^2	$1 + \cos (12 x) = 2 \cos^{2} (12 x)$
19252	Verify the Identity	1+cos(12x)=2cos(6x)^2	$1 + \cos (12 x) = 2 \cos^{2} (6 x)$
19253	Verify the Identity	1+cot(2)x=csc(2)	$1 + \cot (2) x = \csc (2)$
19254	Verify the Identity	1+cos(18x)=2sin(9x)^2	$1 + \cos (18 x) = 2 \sin^{2} (9 x)$
19255	Verify the Identity	1-2cos(x)^2+cos(x)^4=sin(x)^4	$1 - 2 \cos^{2} (x) + \cos^{4} (x) = \sin^{4} (x)$
19256	Verify the Identity	1-(sin(x)^2)/(1-cos(x))=-cos(x)	$1 - \frac{\sin^{2} (x)}{1 - \cos (x)} = - \cos (x)$
19257	Verify the Identity	1-(cos(u)^2)/(1-sin(u))=-sin(u)	$1 - \frac{\cos^{2} (u)}{1 - \sin (u)} = - \sin (u)$
19258	Verify the Identity	square root of 1-sin(x)^2=cos(x)	$\sqrt{1 - \sin^{2} (x)} = \cos (x)$
19259	Verify the Identity	1+cot(-x)^2=csc(x)^2	$1 + \cot^{2} (- x) = \csc^{2} (x)$
19260	Verify the Identity	1+(cos(2x))/(sin(2x))=cot(x)	$1 + \frac{\cos (2 x)}{\sin (2 x)} = \cot (x)$
19261	Verify the Identity	1+(cos(x))/(sin(x))=(sin(x))/(1-cos(x))	$1 + \frac{\cos (x)}{\sin (x)} = \frac{\sin (x)}{1 - \cos (x)}$
19262	Verify the Identity	1+1/(tan(x)^2)=1/(sin(x)^2)	$1 + \frac{1}{\tan^{2} (x)} = \frac{1}{\sin^{2} (x)}$
19263	Verify the Identity	1-tan(x)^2=(cos(2x))/(cos(x)^2)	$1 - \tan^{2} (x) = \frac{\cos (2 x)}{\cos^{2} (x)}$
19264	Verify the Identity	1-(cos(x))/(sec(x))=(sin(x))/(csc(x))	$1 - \frac{\cos (x)}{\sec (x)} = \frac{\sin (x)}{\csc (x)}$
19265	Verify the Identity	1-cot(x)^4=2csc(x)^2-csc(x)^4	$1 - \cot^{4} (x) = 2 \csc^{2} (x) - \csc^{4} (x)$
19266	Verify the Identity	1-(sin(x))/(cos(x))=(cos(x))/(1+sin(x))	$1 - \frac{\sin (x)}{\cos (x)} = \frac{\cos (x)}{1 + \sin (x)}$
19267	Verify the Identity	tan(x)^6=tan(x)^3sec(x)^2-tan(x)^3	$\tan^{6} (x) = \tan^{3} (x) \sec^{2} (x) - \tan^{3} (x)$
19268	Verify the Identity	(tan(x)+tan(y))/(1-tan(x)tan(y))=(cot(x)+cot(y))/(cot(x)cot(y)-1)	$\frac{\tan (x) + \tan (y)}{1 - \tan (x) \tan (y)} = \frac{\cot (x) + \cot (y)}{\cot (x) \cot (y) - 1}$
19269	Verify the Identity	(tan(x)+tan(y))/(cot(x)+cot(y))=tan(x)tan(y)	$\frac{\tan (x) + \tan (y)}{\cot (x) + \cot (y)} = \tan (x) \tan (y)$
19270	Verify the Identity	(tan(x)csc(x))/(sec(x))=1	$\frac{\tan (x) \csc (x)}{\sec (x)} = 1$
19271	Verify the Identity	(tan(x)cot(x))/(cos(x))=sec(x)	$\frac{\tan (x) \cot (x)}{\cos (x)} = \sec (x)$
19272	Verify the Identity	tan(u)^2-sin(u)^2=tan(u)^2sin(u)^2	$\tan^{2} (u) - \sin^{2} (u) = \tan^{2} (u) \sin^{2} (u)$
19273	Verify the Identity	tan(x)^2*sin(x)^2=tan(x)^2-sin(x)^2	$\tan^{2} (x) \cdot \sin^{2} (x) = \tan^{2} (x) - \sin^{2} (x)$
19274	Verify the Identity	tan(x)^2csc(x)^2=sec(x)^2	$\tan^{2} (x) \csc^{2} (x) = \sec^{2} (x)$
19275	Verify the Identity	(tan(x)-tan(y))/(1+tan(x)tan(y))=(sin(x)cos(y)-cos(x)sin(y))/(cos(x)cos(y)+sin(x)sin(y))	$\frac{\tan (x) - \tan (y)}{1 + \tan (x) \tan (y)} = \frac{\sin (x) \cos (y) - \cos (x) \sin (y)}{\cos (x) \cos (y) + \sin (x) \sin (y)}$
19276	Verify the Identity	tan(x)^4+2tan(x)^2+1=sec(x)^4	$\tan^{4} (x) + 2 \tan^{2} (x) + 1 = \sec^{4} (x)$
19277	Verify the Identity	square root of (1+sin(x))/(1-sin(x))=(1+sin(x))/(cos(x))	$\sqrt{\frac{1 + \sin (x)}{1 - \sin (x)}} = \frac{1 + \sin (x)}{\cos (x)}$
19278	Verify the Identity	square root of (1-cos(x))/(1+cos(x))=(1-cos(x))/(\|sin(x)\|)	$\sqrt{\frac{1 - \cos (x)}{1 + \cos (x)}} = \frac{1 - \cos (x)}{\| \sin (x) \|}$
19279	Verify the Identity	(cos(x-y))/(sin(x)sin(y))=cot(x)cot(y)+1	$\frac{\cos (x - y)}{\sin (x) \sin (y)} = \cot (x) \cot (y) + 1$
19280	Verify the Identity	cos(5x)^2-sin(5x)^2=cos(10x)	$\cos^{2} (5 x) - \sin^{2} (5 x) = \cos (10 x)$
19281	Verify the Identity	cos(b)^2-sin(b)^2=2cos(b)^2-1	$\cos^{2} (b) - \sin^{2} (b) = 2 \cos^{2} (b) - 1$
19282	Verify the Identity	cos(x)^2=(csc(x)cos(x))/(tan(x)+cot(x))	$\cos^{2} (x) = \frac{\csc (x) \cos (x)}{\tan (x) + \cot (x)}$
19283	Verify the Identity	cos(x)^2=sin(x/2)^2	$\cos^{2} (x) = \sin^{2} (\frac{x}{2})$
19284	Verify the Identity	(cot(u)+csc(u-1))/(cot(u)-csc(u+1))=csc(u)+cot(u)	$\frac{\cot (u) + \csc (u - 1)}{\cot (u) - \csc (u + 1)} = \csc (u) + \cot (u)$
19285	Verify the Identity	(cot(x))/(1+csc(x))=(csc(x)-1)/(cot(x))	$\frac{\cot (x)}{1 + \csc (x)} = \frac{\csc (x) - 1}{\cot (x)}$
19286	Verify the Identity	(cot(2x))/(1-sin(2t))=(1+tan(x))/(1-tan(x))	$\frac{\cot (2 x)}{1 - \sin (2 t)} = \frac{1 + \tan (x)}{1 - \tan (x)}$
19287	Verify the Identity	(cot(A)-tan(A))/(cot(A)+tan(A))=cos(2A)	$\frac{\cot (A) - \tan (A)}{\cot (A) + \tan (A)} = \cos (2 A)$
19288	Verify the Identity	(cot(a))/(csc(a))=cos(a)	$\frac{\cot (a)}{\csc (a)} = \cos (a)$
19289	Verify the Identity	(cot(A))/(csc(A)+1)=sec(A)-tan(A)	$\frac{\cot (A)}{\csc (A) + 1} = \sec (A) - \tan (A)$
19290	Verify the Identity	(cot(x)+cot(y))/(1-cot(x)cot(y))=(cos(x)sin(y)+sin(x)cos(y))/(sin(x)sin(y)-cos(x)cos(y))	$\frac{\cot (x) + \cot (y)}{1 - \cot (x) \cot (y)} = \frac{\cos (x) \sin (y) + \sin (x) \cos (y)}{\sin (x) \sin (y) - \cos (x) \cos (y)}$
19291	Verify the Identity	(cot(-x))/(csc(x))+cos(x)=0	$\frac{\cot (- x)}{\csc (x)} + \cos (x) = 0$
19292	Verify the Identity	(cot(x))/(csc(x-1))-(csc(x+1))/(cot(x))=0	$\frac{\cot (x)}{\csc (x - 1)} - \frac{\csc (x + 1)}{\cot (x)} = 0$
19293	Verify the Identity	cos(t)^4-sin(t)^4=1-2sin(t)^2	$\cos^{4} (t) - \sin^{4} (t) = 1 - 2 \sin^{2} (t)$
19294	Verify the Identity	cos(x)^2-2sin(x)^2cos(x)^2-sin(x)^2+2sin(x)^4=cos(2x)^2	$\cos^{2} (x) - 2 \sin^{2} (x) \cos^{2} (x) - \sin^{2} (x) + 2 \sin^{4} (x) = \cos^{2} (2 x)$
19295	Verify the Identity	(csc(x)-1)/(csc(x)+1)=(1-sin(x))/(1+sin(x))	$\frac{\csc (x) - 1}{\csc (x) + 1} = \frac{1 - \sin (x)}{1 + \sin (x)}$
19296	Verify the Identity	(csc(x)sin(x))/(cot(x))=tan(x)	$\frac{\csc (x) \sin (x)}{\cot (x)} = \tan (x)$
19297	Verify the Identity	cot(x)^2(sec(x)^2-1)=1	$\cot^{2} (x) (\sec^{2} (x) - 1) = 1$
19298	Verify the Identity	(csc(x))/(sec(x))=cot(x)	$\frac{\csc (x)}{\sec (x)} = \cot (x)$
19299	Verify the Identity	(csc(x))/(1+csc(x))-(csc(x))/(1-csc(x))=2sec(x)^2	$\frac{\csc (x)}{1 + \csc (x)} - \frac{\csc (x)}{1 - \csc (x)} = 2 \sec^{2} (x)$
19300	Verify the Identity	(csc(x))/(1+sec(x))=(cot(x))/(1+cos(x))	$\frac{\csc (x)}{1 + \sec (x)} = \frac{\cot (x)}{1 + \cos (x)}$