Question

Sec² theta - (Sin² theta - 2Sin⁴ theta / 2Cos⁴ theta - Cos² theta) = 1. Please prove this...​

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

Step-by-step explanation:

We have,

$\sec^{2} ( \theta) - \frac{ \sin ^{2} (\theta) - 2 \sin^{4} (\theta) }{2 \cos^{4} (\theta) - \cos ^{2} ( \theta) }$

$= \sec^{2} (\theta) - \frac{ \sin^{2} (\theta)(1 - 2 \sin^{2} (\theta) ) }{ \cos^{2} (\theta)(2 \cos^{2} (\theta) - 1) }$

$= \sec^{2} (\theta) - \frac{ \sin^{2} (\theta)(1 - 2(1 - \cos^{2} (\theta) )) }{ \cos^{2} (\theta)(2 \cos^{2} (\theta) - 1) }$

$= \sec^{2} (\theta) - \frac{ \sin^{2} (\theta)(2 \cos^{2} (\theta) - 1) }{ \cos^{2} (\theta)(2 \cos^{2} (\theta) - 1) }$

$= \sec^{2} ( \theta) - \tan^{2} (\theta)$

$= 1$