First slide

Trigonometric Identities

Question

$\cos e c^{2} A \cot^{2} A - \sec^{2} A \tan^{2} A - (C o t^{2} A - \tan^{2} A) (\sec^{2} A \cos e c^{2} A - 1) =$

Moderate

A

0
B

1
C

2
D

3

Solution

$\frac{\cos^{2} A}{\sin^{4} A} - \frac{\sin^{2} A}{\cos^{4} A} - (\frac{\cos^{2} A}{\sin^{2} A} - \frac{\sin^{2} A}{\cos^{2} A}) (\frac{1}{\sin^{2} A \cos^{2} A} - 1) \frac{\cos^{6} A - \sin^{6} A - (\cos^{4} A - \sin^{4} A) (1 - \sin^{2} A \cos^{2} A)}{\sin^{4} A \cos^{4} A} b u t \cos^{6} A - \sin^{6} A = {(\cos^{2} A)}^{3} - {(\sin^{2} A)}^{3} = (\cos^{2} A - \sin^{2} A) (\cos^{4} A + \sin^{4} A + \cos^{2} A \sin^{2} A) \cos^{4} A + \sin^{4} A = 1 - 2 \sin^{2} A \cos^{2} A \cos^{4} A - \sin^{4} A = (\cos^{2} A + \sin^{2} A) (\cos^{2} A - \sin^{2} A)$

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