Q1. The value of $(1 + \tan^2 A)(1 - \sin A)(1 + \sin A)$ is:
Q2. $9 \sec^2 A - 9 \tan^2 A$ is equal to:
Q3. $(\sec A + \tan A)(1 - \sin A) = $
Q4. Assertion (A): $\sin^2 67^\circ + \cos^2 67^\circ = 1$. Reason (R): For any value of $\theta$, $\sin^2 \theta + \cos^2 \theta = 1$.
Q5. Prove that $\frac{1 - \tan^2 \theta}{1 + \tan^2 \theta} = 1 - 2\sin^2 \theta$.
Solve on white paper.
Q6. Prove that $\sqrt{\frac{1 + \cos \theta}{1 - \cos \theta}} = \csc \theta + \cot \theta$.
Q7. If $\cos \theta + \sin \theta = \sqrt{2} \cos \theta$, show that $\cos \theta - \sin \theta = \sqrt{2} \sin \theta$.
Q8. Prove that $\frac{\tan A + \sec A - 1}{\tan A - \sec A + 1} = \frac{1 + \sin A}{\cos A}$.
Q9. Prove that $\frac{\sin \theta - 2\sin^3 \theta}{2\cos^3 \theta - \cos \theta} = \tan \theta$.
Q10. Prove that $(\sin A + \csc A)^2 + (\cos A + \sec A)^2 = 7 + \tan^2 A + \cot^2 A$.
Q11. Case Study:
Trigonometric identities are equations involving trigonometric functions that are true for every value of the variables involved.
(i) Evaluate $\sin^2 25^\circ + \sin^2 65^\circ$.
(ii) Express the ratio $\cos A$ in terms of $\sin A$.
(iii) Prove that $\sec^4 A - \sec^2 A = \tan^4 A + \tan^2 A$.