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Cofunction identities Problems and solutions

In trigonometry problems, the trigonometric functions are involved in trigonometric expressions and equations. In some cases, one trigonometric function should be converted into another trigonometric function for simplifying the trigonometric expressions or solving the trigonometric equations and the conversion can be done by the cofunction identities. The following is the list of problems with solutions to learn how to use the cofunction identities in trigonometry.

Evaluate $\cos^2{26^\circ}$ $+$ $\cos{64^\circ} \sin{26^\circ}$ $+$ $\dfrac{\tan{36^\circ}}{\cot{54^\circ}}$

Evaluate $\dfrac{5\sin{(17^\circ)}}{\cos{(73^\circ)}}$ $+$ $\dfrac{2\cos{(31^\circ)}}{\sin{(59^\circ)}}$ $-$ $\dfrac{7\sin{(80^\circ)}}{\cos{(10^\circ)}}$

Evaluate $3\dfrac{\sin{72^\circ}}{\cos{18^\circ}}$ $-$ $\dfrac{\sec{32^\circ}}{\csc{58^\circ}}$

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