Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
5801	Find the Exact Value	arccos(sin(-pi/3))	$\arccos (\sin (- \frac{π}{3}))$
5802	Find the Exact Value	arccot(-1/2)	$arccot (- \frac{1}{2})$
5803	Find the Exact Value	arccos(cos(-(5pi)/3))	$\arccos (\cos (- \frac{5 π}{3}))$
5804	Find the Exact Value	arccsc(-9)	$arccsc (- 9)$
5805	Find the Exact Value	arccos(1/4)	$\arccos (\frac{1}{4})$
5806	Find the Exact Value	arccos(2/3)	$\arccos (\frac{2}{3})$
5807	Find the Exact Value	arccos(cos((11pi)/6))	$\arccos (\cos (\frac{11 π}{6}))$
5808	Find the Exact Value	arcsin(0.6)	$\arcsin (0.6)$
5809	Find the Exact Value	arcsin(0.9)	$\arcsin (0.9)$
5810	Find the Exact Value	arcsin(-0.75)	$\arcsin (- 0.75)$
5811	Find the Exact Value	arcsin(-4)	$\arcsin (- 4)$
5812	Find the Exact Value	arcsin(sin((9pi)/8))	$\arcsin (\sin (\frac{9 π}{8}))$
5813	Find the Exact Value	arcsin(pi)	$\arcsin (π)$
5814	Find the Exact Value	arcsin(12/13)	$\arcsin (\frac{12}{13})$
5815	Find the Exact Value	arcsin(2/5)	$\arcsin (\frac{2}{5})$
5816	Find the Exact Value	arcsin(3/4)	$\arcsin (\frac{3}{4})$
5817	Solve for ?	cos(3theta)=-1	$\cos (3 θ) = - 1$
5818	Verify the Identity	tan(x)+cot(x)=2csc(2x)	$\tan (x) + \cot (x) = 2 \csc (2 x)$
5819	Verify the Identity	tan(theta)+cot(t)=2	$\tan (θ) + \cot (t) = 2$
5820	Verify the Identity	tan(x)csc(x)^2-tan(x)=cot(x)	$\tan (x) \csc^{2} (x) - \tan (x) = \cot (x)$
5821	Verify the Identity	tan(-t)=-tan(t)	$\tan (- t) = - \tan (t)$
5822	Verify the Identity	tan(pi/2+x)=-cot(x)	$\tan (\frac{π}{2} + x) = - \cot (x)$
5823	Verify the Identity	sin(x)+sin(x)cot(x)^2=csc(x)	$\sin (x) + \sin (x) \cot^{2} (x) = \csc (x)$
5824	Verify the Identity	sin(x) = square root of 1-cos(x)^2	$\sin (x) = \sqrt{1 - \cos^{2} (x)}$
5825	Verify the Identity	sin(x)cos(x)tan(x)=1-cos(x)^2	$\sin (x) \cos (x) \tan (x) = 1 - \cos^{2} (x)$
5826	Verify the Identity	sin(x+y)sin(x-y)=sin(x)^2-sin(y)^2	$\sin (x + y) \sin (x - y) = \sin^{2} (x) - \sin^{2} (y)$
5827	Verify the Identity	sin(x)+cos(x)=0	$\sin (x) + \cos (x) = 0$
5828	Verify the Identity	sec(x)-tan(x)sin(x)=cos(x)	$\sec (x) - \tan (x) \sin (x) = \cos (x)$
5829	Verify the Identity	sin(x)+cos(x)cot(x)=csc(x)	$\sin (x) + \cos (x) \cot (x) = \csc (x)$
5830	Verify the Identity	sin(x)=( square root of 3)/2	$\sin (x) = \frac{\sqrt{3}}{2}$
5831	Verify the Identity	sec(x)+tan(x)=(1+sin(x))/(cos(x))	$\sec (x) + \tan (x) = \frac{1 + \sin (x)}{\cos (x)}$
5832	Verify the Identity	sec(x)tan(x)(1-sin(x)^2)=sin(x)	$\sec (x) \tan (x) (1 - \sin^{2} (x)) = \sin (x)$
5833	Verify the Identity	sec(y)cos(y)=1	$\sec (y) \cos (y) = 1$
5834	Verify the Identity	csc(x)cos(x)=cot(x)	$\csc (x) \cos (x) = \cot (x)$
5835	Verify the Identity	sin(2x)=-cos(2x)	$\sin (2 x) = - \cos (2 x)$
5836	Verify the Identity	sin(4x)=2sin(2x)cos(2x)	$\sin (4 x) = 2 \sin (2 x) \cos (2 x)$
5837	Verify the Identity	sin(8x)=2sin(4x)cos(4x)	$\sin (8 x) = 2 \sin (4 x) \cos (4 x)$
5838	Verify the Identity	sin(x)(1-2cos(x)^2+cos(x)^4)=sin(x)^5	$\sin (x) (1 - 2 \cos^{2} (x) + \cos^{4} (x)) = \sin^{5} (x)$
5839	Find the Exact Value	14/(sin(51))	$\frac{14}{\sin (51)}$
5840	Find the Exact Value	(1-cos(45))/(sin(45))	$\frac{1 - \cos (45)}{\sin (45)}$
5841	Simplify	(cos(x)^2)(1+tan(x)^2)	$(\cos^{2} (x)) (1 + \tan^{2} (x))$
5842	Expand the Trigonometric Expression	sin(2y)	$\sin (2 y)$
5843	Expand the Trigonometric Expression	sin(2z)	$\sin (2 z)$
5844	Find the Exact Value	(sin(pi/3)cos(pi/4)-sin(pi/4)cos(pi/3))^2	${(\sin (\frac{π}{3}) \cos (\frac{π}{4}) - \sin (\frac{π}{4}) \cos (\frac{π}{3}))}^{2}$
5845	Verify the Identity	(sin(x-y))/(cos(x)sin(y))=tan(x)cot(y)-1	$\frac{\sin (x - y)}{\cos (x) \sin (y)} = \tan (x) \cot (y) - 1$
5846	Verify the Identity	(sin(x)+sin(5x))/(cos(x)+cos(5x))=tan(3x)	$\frac{\sin (x) + \sin (5 x)}{\cos (x) + \cos (5 x)} = \tan (3 x)$
5847	Verify the Identity	sin(x)^2=3cos(x)^2	$\sin^{2} (x) = 3 \cos^{2} (x)$
5848	Verify the Identity	(tan(x)cot(x))/(csc(x))=sin(x)	$\frac{\tan (x) \cot (x)}{\csc (x)} = \sin (x)$
5849	Verify the Identity	(tan(y))/(csc(y))=sec(y)-cos(y)	$\frac{\tan (y)}{\csc (y)} = \sec (y) - \cos (y)$
5850	Verify the Identity	(tan(x)+cot(x))/(tan(x))=csc(x)^2	$\frac{\tan (x) + \cot (x)}{\tan (x)} = \csc^{2} (x)$
5851	Verify the Identity	tan(x)^2-3=0	$\tan^{2} (x) - 3 = 0$
5852	Verify the Identity	tan(x)^2=(1+cos(2x))/(1-cos(2x))	$\tan^{2} (x) = \frac{1 + \cos (2 x)}{1 - \cos (2 x)}$
5853	Verify the Identity	cos(2x)^2+sin(2x)^2=1	$\cos^{2} (2 x) + \sin^{2} (2 x) = 1$
5854	Verify the Identity	(cot(x)-tan(x))/(sin(x)+cos(x))=csc(x)-sec(x)	$\frac{\cot (x) - \tan (x)}{\sin (x) + \cos (x)} = \csc (x) - \sec (x)$
5855	Verify the Identity	(cot(x))/(1+csc(x))+(1+csc(x))/(cot(x))=2sec(x)	$\frac{\cot (x)}{1 + \csc (x)} + \frac{1 + \csc (x)}{\cot (x)} = 2 \sec (x)$
5856	Verify the Identity	cos(y)^2-sin(y)^2=1-2sin(y)^2	$\cos^{2} (y) - \sin^{2} (y) = 1 - 2 \sin^{2} (y)$
5857	Verify the Identity	csc(x)^4-cot(x)^4=csc(x)^2+cot(x)^2	$\csc^{4} (x) - \cot^{4} (x) = \csc^{2} (x) + \cot^{2} (x)$
5858	Verify the Identity	(sin(t))/(tan(t))+(cos(t))/(cot(t))=sin(t)+cos(t)	$\frac{\sin (t)}{\tan (t)} + \frac{\cos (t)}{\cot (t)} = \sin (t) + \cos (t)$
5859	Verify the Identity	(sin(3x))/(sin(x))-(cos(3x))/(cos(x))=2	$\frac{\sin (3 x)}{\sin (x)} - \frac{\cos (3 x)}{\cos (x)} = 2$
5860	Verify the Identity	(sin(2x))/2=(cos(x))/(csc(x))	$\frac{\sin (2 x)}{2} = \frac{\cos (x)}{\csc (x)}$
5861	Verify the Identity	(sec(x)+1)/(tan(x))=(tan(x))/(sec(x)-1)	$\frac{\sec (x) + 1}{\tan (x)} = \frac{\tan (x)}{\sec (x) - 1}$
5862	Verify the Identity	(sec(x)+csc(x))/(tan(x)+cot(x))=sin(x)+cos(x)	$\frac{\sec (x) + \csc (x)}{\tan (x) + \cot (x)} = \sin (x) + \cos (x)$
5863	Verify the Identity	(sec(x))/(cot(x)+tan(x))=sin(x)	$\frac{\sec (x)}{\cot (x) + \tan (x)} = \sin (x)$
5864	Verify the Identity	(sec(x))/(tan(x))=csc(x)	$\frac{\sec (x)}{\tan (x)} = \csc (x)$
5865	Verify the Identity	(sec(x)sin(x))/(tan(x)+cot(x))=sin(x)^2	$\frac{\sec (x) \sin (x)}{\tan (x) + \cot (x)} = \sin^{2} (x)$
5866	Verify the Identity	(sec(t)-cos(t))/(sec(t))=sin(t)^2	$\frac{\sec (t) - \cos (t)}{\sec (t)} = \sin^{2} (t)$
5867	Verify the Identity	cos(x)+cos(2x)=0	$\cos (x) + \cos (2 x) = 0$
5868	Verify the Identity	cos(2x)=cos(x-1)	$\cos (2 x) = \cos (x - 1)$
5869	Verify the Identity	cos(3x)=4cos(x)^3-3cos(x)	$\cos (3 x) = 4 \cos^{3} (x) - 3 \cos (x)$
5870	Verify the Identity	cos(a+b)+cos(a-b)=2cos(a)cos(b)	$\cos (a + b) + \cos (a - b) = 2 \cos (a) \cos (b)$
5871	Verify the Identity	cos(2x)=(1-tan(x)^2)/(1+tan(x)^2)	$\cos (2 x) = \frac{1 - \tan^{2} (x)}{1 + \tan^{2} (x)}$
5872	Verify the Identity	cos(pi/2-x)=sin(x)	$\cos (\frac{π}{2} - x) = \sin (x)$
5873	Verify the Identity	cos(2B-50)=sin(B+30)	$\cos (2 B - 50) = \sin (B + 30)$
5874	Verify the Identity	cos(2x)+cos(x)=0	$\cos (2 x) + \cos (x) = 0$
5875	Verify the Identity	cos(x)csc(x)tan(x)=1	$\cos (x) \csc (x) \tan (x) = 1$
5876	Verify the Identity	cos(x)-cos(x)*sin(x)^2=cos(x)^3	$\cos (x) - \cos (x) \cdot \sin^{2} (x) = \cos^{3} (x)$
5877	Verify the Identity	cos(x+pi/6)+sin(x-pi/3)=0	$\cos (x + \frac{π}{6}) + \sin (x - \frac{π}{3}) = 0$
5878	Verify the Identity	csc(B)-sin(B)=cot(B)cos(B)	$\csc (B) - \sin (B) = \cot (B) \cos (B)$
5879	Verify the Identity	cot(x-y)=(cot(x)cot(y)+1)/(cot(y)-cot(x))	$\cot (x - y) = \frac{\cot (x) \cot (y) + 1}{\cot (y) - \cot (x)}$
5880	Verify the Identity	cot(x)sec(x)^4=cot(x)+2tan(x)+tan(x)^3	$\cot (x) \sec^{4} (x) = \cot (x) + 2 \tan (x) + \tan^{3} (x)$
5881	Verify the Identity	-cot(t)+(sin(t))/(1-cos(t))=csc(t)	$- \cot (t) + \frac{\sin (t)}{1 - \cos (t)} = \csc (t)$
5882	Verify the Identity	arccsc(x)=1/(cos(x))	$arccsc (x) = \frac{1}{\cos (x)}$
5883	Verify the Identity	3tan(x)^3=tan(x)	$3 \tan^{3} (x) = \tan (x)$
5884	Verify the Identity	2cos(2x)- square root of 3=0	$2 \cos (2 x) - \sqrt{3} = 0$
5885	Verify the Identity	2cos(a)cos(b)=cos(a+b)+cos(a-b)	$2 \cos (a) \cos (b) = \cos (a + b) + \cos (a - b)$
5886	Verify the Identity	2sin(2x)^2=1	$2 \sin^{2} (2 x) = 1$
5887	Verify the Identity	2sec(x)^2-2sec(x)^2sin(x)^2-sin(x)^2-cos(x)^2=1	$2 \sec^{2} (x) - 2 \sec^{2} (x) \sin^{2} (x) - \sin^{2} (x) - \cos^{2} (x) = 1$
5888	Verify the Identity	2arccos(x)+pi=4arccos(x)	$2 \arccos (x) + π = 4 \arccos (x)$
5889	Verify the Identity	(sec(x)^2)/(sec(x-1)^2)=csc(x)^2	$\frac{\sec^{2} (x)}{\sec^{2} (x - 1)} = \csc^{2} (x)$
5890	Verify the Identity	(sec(x)^2-1)/(sec(x)^2)=sin(x)^2	$\frac{\sec^{2} (x) - 1}{\sec^{2} (x)} = \sin^{2} (x)$
5891	Verify the Identity	(csc(t)^2)/(cot(t))=csc(t)sec(t)	$\frac{\csc^{2} (t)}{\cot (t)} = \csc (t) \sec (t)$
5892	Verify the Identity	(tan(x)^2)/(sec(x)+1)=(1-cos(x))/(cos(x))	$\frac{\tan^{2} (x)}{\sec (x) + 1} = \frac{1 - \cos (x)}{\cos (x)}$
5893	Verify the Identity	(tan(x)+cot(x))^2=sec(x)^2+csc(x)^2	${(\tan (x) + \cot (x))}^{2} = \sec^{2} (x) + \csc^{2} (x)$
5894	Verify the Identity	(sec(b)-tan(b))^2=(1-(sin(b))/(1+sin(b)))	${(\sec (b) - \tan (b))}^{2} = (1 - \frac{\sin (b)}{1 + \sin (b)})$
5895	Verify the Identity	(sin(x))(tan(x)cos(x)-cot(x)cos(x))=1-2cos(x)^2	$(\sin (x)) (\tan (x) \cos (x) - \cot (x) \cos (x)) = 1 - 2 \cos^{2} (x)$
5896	Verify the Identity	(1-cos(x))(1+cos(x))=1/(1+cot(x)^2)	$(1 - \cos (x)) (1 + \cos (x)) = \frac{1}{1 + \cot^{2} (x)}$
5897	Verify the Identity	(csc(x)+cot(x))(csc(x)-cot(x))=1	$(\csc (x) + \cot (x)) (\csc (x) - \cot (x)) = 1$
5898	Verify the Identity	(tan(x)^2+1)(cos(x)^2-1)=-tan(x)^2	$(\tan^{2} (x) + 1) (\cos^{2} (x) - 1) = - \tan^{2} (x)$
5899	Verify the Identity	(1-cos(x))/(sin(x))+(sin(x))/(1-cos(x))=2csc(x)	$\frac{1 - \cos (x)}{\sin (x)} + \frac{\sin (x)}{1 - \cos (x)} = 2 \csc (x)$
5900	Verify the Identity	(1+sin(x))/(1-sin(x))-(1-sin(x))/(1+sin(x))=4tan(x)sec(x)	$\frac{1 + \sin (x)}{1 - \sin (x)} - \frac{1 - \sin (x)}{1 + \sin (x)} = 4 \tan (x) \sec (x)$