Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
19001	Verify the Identity	tan(x)+cot(x)=1/(sin(xcos(x)))	$\tan (x) + \cot (x) = \frac{1}{\sin (x \cos (x))}$
19002	Verify the Identity	tan(x)+cos(x)=sec(x)csc(x)	$\tan (x) + \cos (x) = \sec (x) \csc (x)$
19003	Verify the Identity	sin(x-y)sin(x+y)=sin(x)^2-sin(y)^2	$\sin (x - y) \sin (x + y) = \sin^{2} (x) - \sin^{2} (y)$
19004	Verify the Identity	tan(x)+cot(x)=sec(x)+csc(x)	$\tan (x) + \cot (x) = \sec (x) + \csc (x)$
19005	Verify the Identity	tan(x)-cot(x)=(sin(x)^2-cos(x)^2)/(sin(x)cos(x))	$\tan (x) - \cot (x) = \frac{\sin^{2} (x) - \cos^{2} (x)}{\sin (x) \cos (x)}$
19006	Verify the Identity	tan(x)=-24/7	$\tan (x) = - \frac{24}{7}$
19007	Verify the Identity	sin(x)+cos(3x)=0	$\sin (x) + \cos (3 x) = 0$
19008	Verify the Identity	sin(x)+cos(x)*cot(x)=csc(x)	$\sin (x) + \cos (x) \cdot \cot (x) = \csc (x)$
19009	Verify the Identity	sin(x)=sin(-x)	$\sin (x) = \sin (- x)$
19010	Verify the Identity	sin(x)=tan(x)cos(x)	$\sin (x) = \tan (x) \cos (x)$
19011	Verify the Identity	sin(x)=cos(2x)	$\sin (x) = \cos (2 x)$
19012	Verify the Identity	sin(x)=1/(csc(x))	$\sin (x) = \frac{1}{\csc (x)}$
19013	Verify the Identity	sin(-x)-sin(x)=1	$\sin (- x) - \sin (x) = 1$
19014	Verify the Identity	sin(x)cos(y)=1/2*(sin(x+y)+sin(x-y))	$\sin (x) \cos (y) = \frac{1}{2} \cdot (\sin (x + y) + \sin (x - y))$
19015	Verify the Identity	sin(x)cot(x)sec(x)=1	$\sin (x) \cot (x) \sec (x) = 1$
19016	Verify the Identity	sin(x)-cos(x)=1-2sin(x)cos(x)	$\sin (x) - \cos (x) = 1 - 2 \sin (x) \cos (x)$
19017	Verify the Identity	sin(x)cos(x)=sin(x)	$\sin (x) \cos (x) = \sin (x)$
19018	Verify the Identity	sin(x)tan(x)-sin(x)=0	$\sin (x) \tan (x) - \sin (x) = 0$
19019	Verify the Identity	sin(x-(3pi)/2)=-sin(x)	$\sin (x - \frac{3 π}{2}) = - \sin (x)$
19020	Verify the Identity	sin(x-pi/4)=( square root of 2)/2	$\sin (x - \frac{π}{4}) = \frac{\sqrt{2}}{2}$
19021	Verify the Identity	sin(x+180/2)=cos(x)	$\sin (x + \frac{180}{2}) = \cos (x)$
19022	Verify the Identity	sin(x+pi/3)+sin(x-pi/3)=( square root of 3)/2	$\sin (x + \frac{π}{3}) + \sin (x - \frac{π}{3}) = \frac{\sqrt{3}}{2}$
19023	Verify the Identity	sin(x+pi/3)+sin(x-pi/3)=1	$\sin (x + \frac{π}{3}) + \sin (x - \frac{π}{3}) = 1$
19024	Verify the Identity	sin(x+60)=2cos(x-30)	$\sin (x + 60) = 2 \cos (x - 30)$
19025	Verify the Identity	sin(x+pi)=sin(x)	$\sin (x + π) = \sin (x)$
19026	Verify the Identity	sec(x)-tan(x)=(1-sin(x))/(cos(x))	$\sec (x) - \tan (x) = \frac{1 - \sin (x)}{\cos (x)}$
19027	Verify the Identity	sin(x)+tan(-x)=0	$\sin (x) + \tan (- x) = 0$
19028	Verify the Identity	sin(x)+cos(x)-cot(x)=sec(x)	$\sin (x) + \cos (x) - \cot (x) = \sec (x)$
19029	Verify the Identity	sin(x)(sin(3x)+sin(5x))=cos(x)(cos(3x)-cos(5x))	$\sin (x) (\sin (3 x) + \sin (5 x)) = \cos (x) (\cos (3 x) - \cos (5 x))$
19030	Verify the Identity	sin(-x)=-sin(x)	$\sin (- x) = - \sin (x)$
19031	Verify the Identity	sin(x)csc(x)=1	$\sin (x) \csc (x) = 1$
19032	Verify the Identity	sec(x)*csc(x)+tan(x)=cot(x)	$\sec (x) \cdot \csc (x) + \tan (x) = \cot (x)$
19033	Verify the Identity	sec(t)-cos(t)=sin(t)tan(t)	$\sec (t) - \cos (t) = \sin (t) \tan (t)$
19034	Verify the Identity	sec(u)+tan(u)=(cos(u))/(1-sin(u))	$\sec (u) + \tan (u) = \frac{\cos (u)}{1 - \sin (u)}$
19035	Verify the Identity	sec(B)-cos(B)=sin(B)tan(B)	$\sec (B) - \cos (B) = \sin (B) \tan (B)$
19036	Verify the Identity	sec(-x)-sin(-x)tan(-x)=cos(x)	$\sec (- x) - \sin (- x) \tan (- x) = \cos (x)$
19037	Verify the Identity	sec(x)=- square root of 2	$\sec (x) = - \sqrt{2}$
19038	Verify the Identity	r=cos(x)	$r = \cos (x)$
19039	Verify the Identity	r=sin(2x)	$r = \sin (2 x)$
19040	Verify the Identity	f(2-x)=cos(2-x)^2	$f (2 - x) = \cos^{2} (2 - x)$
19041	Verify the Identity	r=-12sin(x)	$r = - 12 \sin (x)$
19042	Verify the Identity	r-6sin(x)=2cos(x)	$r - 6 \sin (x) = 2 \cos (x)$
19043	Verify the Identity	sec(2x)=(csc(x)^2)/(csc(x)^2-2)	$\sec (2 x) = \frac{\csc^{2} (x)}{\csc^{2} (x) - 2}$
19044	Verify the Identity	sec(2x)=(csc(x)^2)/(2cot(x)^2-csc(x)^2)	$\sec (2 x) = \frac{\csc^{2} (x)}{2 \cot^{2} (x) - \csc^{2} (x)}$
19045	Verify the Identity	sec(x/2)=cos(x/2)	$\sec (\frac{x}{2}) = \cos (\frac{x}{2})$
19046	Verify the Identity	sec(x^4)-sec(x^2)=tan(x^4)-tan(x^2)	$\sec (x^{4}) - \sec (x^{2}) = \tan (x^{4}) - \tan (x^{2})$
19047	Verify the Identity	sec(2x)=1/(1-2sin(x)^2)	$\sec (2 x) = \frac{1}{1 - 2 \sin^{2} (x)}$
19048	Verify the Identity	csc(x)sec(x)=1/(sin(x)cos(x))	$\csc (x) \sec (x) = \frac{1}{\sin (x) \cos (x)}$
19049	Verify the Identity	csc(x)sin(x)-sin(x)^2=cos(x)^2	$\csc (x) \sin (x) - \sin^{2} (x) = \cos^{2} (x)$
19050	Verify the Identity	csc(y)-cos(y)cot(y)=sin(y)	$\csc (y) - \cos (y) \cot (y) = \sin (y)$
19051	Verify the Identity	csc(x)cos(x)tan(x)=1	$\csc (x) \cos (x) \tan (x) = 1$
19052	Verify the Identity	csc(x)-cot(x)=1/(csc(x)+cot(x))	$\csc (x) - \cot (x) = \frac{1}{\csc (x) + \cot (x)}$
19053	Verify the Identity	csc(x)-cot(x)cos(x)=sin(x)	$\csc (x) - \cot (x) \cos (x) = \sin (x)$
19054	Verify the Identity	csc(-x)=-csc(x)	$\csc (- x) = - \csc (x)$
19055	Verify the Identity	sin(2A)=cos(3A)	$\sin (2 A) = \cos (3 A)$
19056	Verify the Identity	sin(2x)=3/5	$\sin (2 x) = \frac{3}{5}$
19057	Verify the Identity	sin(pi/6+x)+sin(pi/6-x)=cos(x)	$\sin (\frac{π}{6} + x) + \sin (\frac{π}{6} - x) = \cos (x)$
19058	Verify the Identity	sin(x/2)=2sin(x/2)^2	$\sin (\frac{x}{2}) = 2 \sin^{2} (\frac{x}{2})$
19059	Verify the Identity	sin(x/2)=-cos(x/2)	$\sin (\frac{x}{2}) = - \cos (\frac{x}{2})$
19060	Verify the Identity	sin(2x)=2cot(x)sin(x)^2	$\sin (2 x) = 2 \cot (x) \sin^{2} (x)$
19061	Verify the Identity	sin(2x)=0	$\sin (2 x) = 0$
19062	Verify the Identity	sin(2pi-x)=-sin(x)	$\sin (2 π - x) = - \sin (x)$
19063	Verify the Identity	sin(2x)=(tan(x))(1+cos(2x))	$\sin (2 x) = (\tan (x)) (1 + \cos (2 x))$
19064	Verify the Identity	sin(2x)cos(x)+cos(2x)sin(x)=-( square root of 3)/2	$\sin (2 x) \cos (x) + \cos (2 x) \sin (x) = - \frac{\sqrt{3}}{2}$
19065	Verify the Identity	sin(2x)cos(2x)=sin(2x)-4(sin(x)sin(x)sin(x))cos(x)	$\sin (2 x) \cos (2 x) = \sin (2 x) - 4 (\sin (x) \sin (x) \sin (x)) \cos (x)$
19066	Verify the Identity	sin(2x)=tan(x)+tan(x)cos(2x)	$\sin (2 x) = \tan (x) + \tan (x) \cos (2 x)$
19067	Verify the Identity	sin(1/2A-cos(1/2A)) = square root of 1-sin(A)	$\sin (\frac{1}{2} A - \cos (\frac{1}{2} A)) = \sqrt{1 - \sin (A)}$
19068	Verify the Identity	sin((7pi)/6+x)-cos((2pi)/3+x)=0	$\sin (\frac{7 π}{6} + x) - \cos (\frac{2 π}{3} + x) = 0$
19069	Verify the Identity	sin(x/2)cos(x/2)=(sin(x))/2	$\sin (\frac{x}{2}) \cos (\frac{x}{2}) = \frac{\sin (x)}{2}$
19070	Verify the Identity	sin(pi/3+x)-cos(pi/6+x)=sin(x)	$\sin (\frac{π}{3} + x) - \cos (\frac{π}{6} + x) = \sin (x)$
19071	Verify the Identity	sin(arcsin(x))=arcsin(sin(x))	$\sin (\arcsin (x)) = \arcsin (\sin (x))$
19072	Verify the Identity	sin(120)-sin(90)=sin(30)	$\sin (120) - \sin (90) = \sin (30)$
19073	Verify the Identity	sin(3x)-(sin(x))÷(cos(1^2))x-sin(1^2)=2sin(x)	$\sin (3 x) - \sin (x) \div \cos (1^{2}) x - \sin (1^{2}) = 2 \sin (x)$
19074	Verify the Identity	sin(2x)-sin(4x)=0	$\sin (2 x) - \sin (4 x) = 0$
19075	Verify the Identity	sin(2x)sin(x)=cos(x)	$\sin (2 x) \sin (x) = \cos (x)$
19076	Verify the Identity	sin(2x)-cot(x)=-cot(x)cos(2x)	$\sin (2 x) - \cot (x) = - \cot (x) \cos (2 x)$
19077	Verify the Identity	sin(3x)=1/2	$\sin (3 x) = \frac{1}{2}$
19078	Verify the Identity	sin(3x+13)=cos(4x)	$\sin (3 x + 13) = \cos (4 x)$
19079	Verify the Identity	sin(6x)cos(2x)-cos(6x)sin(2x)=2sin(2x)cos(2x)	$\sin (6 x) \cos (2 x) - \cos (6 x) \sin (2 x) = 2 \sin (2 x) \cos (2 x)$
19080	Verify the Identity	sin(6x)tan(3x)=2sin(3x)^2	$\sin (6 x) \tan (3 x) = 2 \sin^{2} (3 x)$
19081	Verify the Identity	sin(4x)-sin(2x)=0	$\sin (4 x) - \sin (2 x) = 0$
19082	Verify the Identity	sin(3x)=sin(x)-sin(2x)	$\sin (3 x) = \sin (x) - \sin (2 x)$
19083	Verify the Identity	sin(3x)cos(3x)=1/2*sin(6x)	$\sin (3 x) \cos (3 x) = \frac{1}{2} \cdot \sin (6 x)$
19084	Verify the Identity	sin(4x)=4sin(x)cos(x)^3-4sin(x)^3cos(x)	$\sin (4 x) = 4 \sin (x) \cos^{3} (x) - 4 \sin^{3} (x) \cos (x)$
19085	Verify the Identity	sin(4x)=8cos(x)^3sin(x)-4cos(x)sin(x)	$\sin (4 x) = 8 \cos^{3} (x) \sin (x) - 4 \cos (x) \sin (x)$
19086	Verify the Identity	sin(4x)=8sin(x)cos(x)^3-4sin(x)cos(x)	$\sin (4 x) = 8 \sin (x) \cos^{3} (x) - 4 \sin (x) \cos (x)$
19087	Verify the Identity	sin(4u)=2sin(2u)cos(2u)	$\sin (4 u) = 2 \sin (2 u) \cos (2 u)$
19088	Verify the Identity	sin(pi-x)=-sin(x)	$\sin (π - x) = - \sin (x)$
19089	Verify the Identity	sin(pi-t)=sin(t)	$\sin (π - t) = \sin (t)$
19090	Verify the Identity	sin(theta)=sin(2theta)	$\sin (t h e t a) = \sin (2 t h e t a)$
19091	Verify the Identity	sin(a)sin(b)=(1/2)(cos(a-b)-cos(a+b))	$\sin (a) \sin (b) = (\frac{1}{2}) (\cos (a - b) - \cos (a + b))$
19092	Verify the Identity	sin(a)sin(b)=1/2*(cos(a-b)-cos(a+b))	$\sin (a) \sin (b) = \frac{1}{2} \cdot (\cos (a - b) - \cos (a + b))$
19093	Verify the Identity	sin(-a)+sin(pi/2-a)+cos(a-pi/2)=cos(2pi-a)	$\sin (- a) + \sin (\frac{π}{2} - a) + \cos (a - \frac{π}{2}) = \cos (2 π - a)$
19094	Verify the Identity	sin(90+x)=cos(x)	$\sin (90 + x) = \cos (x)$
19095	Verify the Identity	sin(a+B)-sin(a-b)=2cos(a)sin(b)	$\sin (a + B) - \sin (a - b) = 2 \cos (a) \sin (b)$
19096	Verify the Identity	sin(a+b)=sin(a)cos(b)+cos(a)sin(b)	$\sin (a + b) = \sin (a) \cos (b) + \cos (a) \sin (b)$
19097	Verify the Identity	sin(B)+cos(B)cot(B)=csc(B)	$\sin (B) + \cos (B) \cot (B) = \csc (B)$
19098	Find the Exact Value	5/(sin(30))	$\frac{5}{\sin (30)}$
19099	Find the Exact Value	50/(tan(53))	$\frac{50}{\tan (53)}$
19100	Find the Exact Value	5/(sin(45))	$\frac{5}{\sin (45)}$