# Trigonometry Problems - sin, cos, tan, cot: Problems with Solutions

Problem 1
sin(A) =

Problem 2
tan(A) =

Problem 3
cot(A) =

Problem 4
sin(30°)=
Problem 5
cos(90°) =
Problem 6
sin2(43°) + cos2(43°) =
Problem 7
Find $$\cos\alpha$$, $$\tan\alpha$$, $$\cot\alpha$$, if $$\sin\alpha = {\frac{5}{13}}$$ and $${\frac{\pi}{2}} < \alpha < \pi$$.
Problem 8
Find $\cot(\pi + x) = ?$
Problem 9
Calculate sin(-585°).
Problem 10
Calculate $\tan(270^{\circ}+\alpha)$.

Problem 11
Find the exact value of $$cos{\frac{8\pi}{3}} = ?$$.
Problem 12
Calculate $$\sin 945^{\circ}$$.
Problem 13
cos(24°) + cos(5°) + cos(175°) + cos(204°) + cos(300°) =
Problem 14 sent by Vasa Shanmukha Reddy
If cot(x) = 2 then find $\frac{(2+2\sin x)(1-\sin x)}{(1+\cos x)(2-2\cos x)}$
Problem 15
Find the exact value of cos 15°.
Problem 16
Calculate sin75°sin15° =
Problem 17
Calculate the exact value of sin15°.
Problem 18
Find the exact value of sin4α+cos4αcot2α, if tan2α=4.
Problem 19
Simplify
3+4cos2α+cos4α
Problem 20
Prove the trigonometric identity
$$4cos({\frac{\pi}{6}}-\alpha)sin({\frac{\pi}{3}}-\alpha)=({\frac{sin3\alpha}{sin\alpha}})$$
Problem 21
Simplify $${\frac{sin\alpha}{1+cos\alpha}}+{\frac{1+cos\alpha}{sin\alpha}}$$
Problem 22
Prove the trigonometric identity: $$cos\alpha+cos2\alpha+cos6\alpha+cos7\alpha=4cos\alpha{\frac{\alpha}{2}}cos{\frac{5\alpha}{2}}cos4\alpha$$

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