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

Trigonometry problems with solutions.
Problem 1
sin2(43°) + cos2(43°) =
Problem 2
Find [tex]\cos\alpha[/tex], [tex]\tan\alpha[/tex], [tex]\cot\alpha[/tex], if [tex]\sin\alpha = {\frac{5}{13}}[/tex] and [tex]{\frac{\pi}{2}} < \alpha < \pi[/tex].
Problem 3
Find $\cot(\pi + x) = ?$
Problem 4
Calculate sin(-585°).
Problem 5
Calculate tan(270°+α).
Problem 6
Find the exact value of [tex]cos{\frac{8\pi}{3}} = ?[/tex].
Problem 7
Calculate [tex]sin 945^{\circ}[/tex].
Problem 8
cos(24°) + cos(5°) + cos(175°) + cos(204°) + cos(300°) =
Problem 9 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 10
Find the exact value of cos 15°.

Problem 11
Calculate sin75°sin15° =
Problem 12
Calculate the exact value of sin15°.
Problem 13
Find the exact value of sin4α+cos4αcot2α, if tan2α=4.
Problem 14
Simplify
3+4cos2α+cos4α
Problem 15
Prove the trigonometric identity
[tex]4cos({\frac{\pi}{6}}-\alpha)sin({\frac{\pi}{3}}-\alpha)=({\frac{sin3\alpha}{sin\alpha}})[/tex]
Problem 16
Simplify [tex]{\frac{sin\alpha}{1+cos\alpha}}+{\frac{1+cos\alpha}{sin\alpha}}[/tex]
Problem 17
Prove the trigonometric identity: cosα+cos2α+cos6α+cos7α=[tex]4cos\alpha{\frac{\alpha}{2}}cos{\frac{5\alpha}{2}}cos4\alpha[/tex]
Problem 18
Solve the trigonometric equation: [tex]tan3x={\frac{1}{tan2x}}[/tex].
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