Question

If sin^–1a + sin^–1b + sin^–1c = π, then find the value of `asqrt(1 - a^2) + bsqrt(1 - b^2) + csqrt(1 - c^2)`.

Options

• abc

• a + b + c

• `1/a xx 1/b xx 1/c`

• 2abc

Answer 1

2abc

Explanation:

Let sin^–1a = x 

∴ a = sin x

sin^–1b = y   

∴ b = sin y; sin^–1c = z

∴ c = sin z

∴ `asqrt(1 - a^2) + bsqrt(1 - b^2) + csqrt(1 - c^2)`

= sin x cos x + sin y cosy + sin z cos z

= (1/2)(sin 2x + sin 2y + sin 2z)

= (1/2) (4sinx siny sinz)

= 2 sin x sin y sin z

= 2abc