If cos –1 p + cos –1 q + cos –1 r = π . Then value of p 2 +…

Maths Inverse Trigonometric Functions Mix Single Correct MCQ

Published by: CGP EDU Academic Team

Published on: August 14, 2026

If cos –1 p + cos –1 q + cos –1 r = π . Then value of p 2 + q 2 + r 2 + 2pqr + 4 is equal to-

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The correct answer is:

Let cos –1 p = α , cos –1 q = β , cos –1 r = γ

cos α = p, cos β = q, cos γ = r , α + β + γ = π

cos ( α + β ) = cos ( π – γ )

⇒ cos α .cos β – sin α sin β = –cos γ

⇒ pq – = – r

⇒ p 2 + q 2 + r 2 + 2pqr = 1

⇒ p 2 + q 2 + r 2 + 2pqr + 4 = 5.

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