Without using trigonometric tables, evaluate. 35^ 55^ + 35^ 55^ c… - Vidyadip

Question

Without using trigonometric tables, evaluate.
$\frac{\sin 35^{\circ} \cos 55^{\circ}+\cos 35^{\circ} \sin 55^{\circ}}{\operatorname{cosec}^2 10^{\circ}-\tan ^2 80^{\circ}}$

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Answer

1
\[\left[\text { Hint . Given exp. }=\frac{\sin (90-55) \cos 55+\cos (90-55) \sin 55}{\operatorname{cosec}^2(90-80)^2-\tan ^2 80}\right] .\]

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