Question

solve this question

Answer 1

This question is related to the relation between different trigonometric ratios and does not deal much with the trigonometric identities. These type of questions gradually get simplified in each step and end up in small whole numbers.

$\sf \frac{ \sin25 \degree }{ \cos65 \degree } + \frac{ \cot15 \degree }{ \tan75 \degree } + \frac{2 \cos43 \degree \csc47 \degree }{ \tan10 \degree \tan40 \degree \tan50 \degree \tan80 \degree } \\ \\ \sf \implies \: \frac{ \sin25 \degree }{ \sin(90 \degree - 65 \degree) } + \frac{ \cot15 \degree }{ \cot(90 \degree - 75 \degree ) } + \frac{2 \cos43 \degree \sec(90 \degree - 47 \degree) }{ \tan10 \degree \tan40 \degree \cot(90 \degree - 50 \degree) \cot(90 \degree - 80 \degree) } \\ \\ \sf \implies \: \: \frac{ \cancel{\sin25 \degree}}{ \cancel{\sin25 \degree}} + \frac{ \cancel{ \cot15 \degree}}{ \cancel{ \cot15 \degree}} + \frac{2 \cancel{\cos43 \degree} \times \frac{1}{ \cancel {\cos43 \degree}} }{ \cancel{ \tan10 \degree} \cancel{\tan40 \degree} \cancel{ \cot40 \degree} \cancel{ \cot10 \degree}} \\ \\ \sf \implies \: 1 + 1 + 2 \\ \\ \implies \sf \: 4$

Thus, the evaluation of this trigonometric equation is 4.

Answer 2

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