Question

Secant squared theta minus cos square theta = sin square theta into secant squared theta + 1 prove that

Answer 1

We know that,

$\sin^2\theta+\cos^2\theta=1 \\ \\ \therefore\ \sin^2\theta=1-\cos^2\theta$

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

Hence proved!

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Answer 2

Step-by-step explanation:

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