Exam Questions & Step-by-Step Markschemes (67 Problems)
Question 1 • 2023
4 Marks
Prove that: \frac{\sin \theta - 2\sin^3 \theta}{2\cos^3 \theta - \cos \theta} = \tan \theta
Answer: \tan \theta \quad (AG)
Question 2 • 2024
5 Marks
Prove that: \frac{\sin\theta - \cos\theta + 1}{\sin\theta + \cos\theta - 1} = \frac{1}{\sec\theta - \tan\theta} .
Answer: \text{LHS} = \text{RHS} \quad (\text{Proved})
Question 3 • 2023
4 Marks
Prove the following trigonometric identity: \frac{\tan \theta}{1 - \cot \theta} + \frac{\cot \theta}{1 - \tan \theta} = 1 + \sec \theta \csc \theta
Answer: \text{Hence Proved, } \text{LHS} = 1 + \sec \theta \csc \theta
Question 4 • 2023
4 Marks
Prove the identity: \frac{\sin\theta - 2\sin^3\theta}{2\cos^3\theta - \cos\theta} = \tan\theta
Answer: \text{LHS} = \text{RHS} = \tan\theta
Question 5 • 2023
1 Marks
If \tan A = \frac{3}{4} , then the value of \frac{4 \sin A-2 \cos A}{4 \sin A + 2 \cos A} is :
Answer: (b) \frac{1}{5}
Question 6 • 2023
1 Marks
If 2 \tan A = 3 , then the value of \frac{4 \sin A +3 \cos A}{4 \sin A-3 \cos A} is
Answer: Option (C) : 3