Question
Evaluate:$\frac{\cot ^2 41^{\circ}}{\tan ^2 49^{\circ}}-2 \frac{\sin ^2 75^{\circ}}{\cos ^2 15^{\circ}}$
✓
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}} $
$=\frac{\tan ^2 49^{\circ}}{\tan ^2 59^{\circ}}-2 \frac{\cos ^2 15^{\circ}}{\cos ^2 15^{\circ}}$
$= 1 - 2$
$= -1$
$ =\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}} $
$=\frac{\tan ^2 49^{\circ}}{\tan ^2 59^{\circ}}-2 \frac{\cos ^2 15^{\circ}}{\cos ^2 15^{\circ}}$
$= 1 - 2$
$= -1$
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