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Question
Prove the following trigonometric identities:
`((1 + sin theta)^2 + (1 - sin theta)^2)/(2cos^2 theta) = (1 + sin^2 theta)/(1 - sin^2 theta)`
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Solution
LHS = `(1 sin^2 theta + 2 sin theta + 1 + sin^2 theta - 2 sin theta)/(2 cos theta)`
`=> (2(1 + sin^2 theta))/(2 cos^2 theta) => (1 + sin^2 theta)/(1 - sin^2 theta)` `[∵ cos^2 theta = 1 - sin^2 theta]`
∴ LHS = RHS Hence proved
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