Question

If in ∆ ABC, ∠A = sin^-1(x), ∠B = sin^-1(y) and ∠C = sin^-1(z), then x√(1 - y²)√(1 - z²) + y√(1 - x²)√(1 - z²) + z√(1 - x²)√(1 - y²) is equal to

(A) xyz

(B) x + y + z

(C) 1/x + 1/y + 1/z 

(D) None of these

Answer 1

Correct option (A) xyz

Explanation:

Given

x = sin A, y = sin B, z = sin C

Now, sinA cosB cosC + sinB cosA cosC + sinC cos AcosB

- sinA sinB sinC = sin(A + B + C) = sin nπ = 0

Therefore, given expression = sinA sinB sinC = xyz.