29. Which of the following is true for all values of \( \theta\left(0^{\circ} \leq \theta \leq 90^{\circ}\right) \) ? (a) \( \cos ^{2} \theta-\sin ^{2} \theta=1 \) (b) \( \operatorname{cosec}^{2} \theta-\sec ^{2} \theta=1 \) (c) \( \sec ^{2} \theta-\tan ^{2} \theta=1 \) (d) \( \cot ^{2} \theta-\tan ^{2} \theta=1 \) (2023)
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The identity \( \cos^2 \theta + \sin^2 \theta = 1 \) is true for all \( \theta \). Rearranging gives \( \cos^2 \theta - \sin^2 \theta = \cos^2 \theta - (1 - \cos^2 \theta) = 2\cos^2 \theta - 1 \), which is not equal to 1 for all \( \theta \). Show more…
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