Question

If cos^–1 p + cos^–1 q + cos^–1

r = p. Then value of p² + q² + r² + 2pqr + 4 is equal to-

• A. 1
• B. 0
• C. 5
• D. 3

Answer 1

Answer: (C)

5

Answer 2

Let cos^–1 p = a, cos^–1q = b, cos^–1 r = g

cos a = p, cos b = q, cos g = r ,a + b + g = p

cos (a + b) = cos (p – g)

Ž cos a.cos b – sin a sin b = –cos g

Ž pq – = – r

Ž p² + q² + r² + 2pqr = 1

Ž p² + q² + r² + 2pqr + 4 = 5.