Question

The value of `sin^-1 (cos  (3π)/5)` is ______.

Options

• `π/10`

• `(3π)/5`

• `- π/10`

• `(-3π)/5`

Answer 1

The value of `sin^-1 (cos  (3π)/5)` is `underlinebb(- π/10)`.

Explanation:

`sin^-1 [cos((3π)/5)]`

= `sin^-1[cos(π/2 + π/10)]`

= `sin^-1(-sin  π/10)`   ...`[∵ cos(π/2 + x) = -sin x]`

= `-sin^-1 (sin  π/10)`   ...[∵ sin^–1(–x) = – sin^–1x]

= `- π/10`   ...`[∵ sin^-1 (sin x) = x, x ∈ ((-π)/2, π/2)]`