Evaluate : ^2 41^ ^2 49^ -2 ^2 75^ ^2 15^ - Vidyadip

Question

Evaluate : $\frac{\cot ^2 41^{\circ}}{\tan ^2 49^{\circ}}-2 \frac{\sin ^2 75^{\circ}}{\cos ^2 15^{\circ}}$

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Answer

$\frac{\cot ^2 41^{\circ}}{\tan ^2 49^{\circ}}-2 \frac{\sin ^2 75^{\circ}}{\cos ^2 15^{\circ}}$
$=\frac{\left(\cot \left(90^{\circ}-49^{\circ}\right)\right)^2}{\tan ^2 49^{\circ}}-2 \frac{\left(\sin \left(90^{\circ}-15^{\circ}\right)\right)^2}{\cos ^2 15^{\circ}}$
$=\frac{\tan ^2 49^{\circ}}{\tan ^2 49^{\circ}}-2 \frac{\cos ^2 15^{\circ}}{\cos ^2 15^{\circ}}$
$=1-2=-1$

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