If tan –1 (sin 2 θ + 2 sin θ + 2) + cot –1 = has solution…

Maths Inverse Trigonometric Functions Inverse Trigonometric Functions, Inverse Trigo Identities Single Correct MCQ

Published by: CGP EDU Academic Team

Published on: August 12, 2026

If tan –1 (sin 2 θ + 2 sin θ + 2) + cot –1 = has solution for some θ and φ then

sin θ = –1

sin θ = 1

cos φ = 1

cos φ = –1

Text Solution

Verified by Experts

The correct answer is:

CHECK THE SOLUTION.

(a, c, d)

The equation holds if

sin 2 θ + 2 sin θ + 2 =

Now L.H.S. = (sin θ + 1) 2 + 1 ≤ 5 and R.H.S. ≥ 5

(  sec 2 φ ≥ 1) So, L.H.S. = R.H.S.

⇒ sin θ = – 1 and sec 2 φ = 1

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