If sin(x + y) = cos {3(x + y)}, then, the value of cot {2(x + y)} is _______.

Question

Question

This question was previously asked in

SSC CPO 2024 Official Paper-I (Held On: 29 Jun, 2024 Shift 2)

Answer 1

Given:

If sin(x + y) = cos {3(x + y)}

Formula used:

sin A = cos B ⟹ A + B = π/2

Calculation:

Let A = x + y and B = 3(x + y)

⇒ A + B = π/2

⇒ (x + y) + 3(x + y) = π/2

⇒ 4(x + y) = π/2

⇒ x + y = π/8

Now, we need to find the value of cot {2(x + y)}

⇒ 2(x + y) = 2 × π/8

⇒ 2(x + y) = π/4

cot (π/4) = 1

∴ The correct answer is option (2).

Download Solution PDF