b) \( \frac{1-\cos ^{2} \theta}{1-\sin ^{2} \theta} \)
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Step 1: Recall the Pythagorean identity: \[ \sin^2 \theta + \cos^2 \theta = 1 \] Show more…
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$\left(\frac{1+\sin \theta-\cos \theta}{1+\sin \theta+\cos \theta}\right)^{2}$ is equal to (a) $\frac{1-\cos \theta}{1+\cos \theta}$ (b) $\frac{1-\sin \theta}{1+\sin \theta}$ (c) $\tan ^{2} \frac{\theta}{2}$ (d) $\cot ^{2} \frac{\theta}{2}$
Value of the expression $\frac{\sin \theta}{1+\cos \theta}+\frac{\cos \theta}{1-\sin \theta}$ is (a) $\sqrt{2} \sin \left(\frac{\pi}{4}+\theta\right)$ (b) $\sqrt{2} \cos \left(\frac{\pi}{4}-\theta\right)$ (c) $\sqrt{2} \sin \left(\frac{\pi}{4}-\theta\right)$ (d) $\sqrt{2} \cos \left(\frac{\pi}{4}+\theta\right)$
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