Question

The value of cos (2cos^–1 x + sin^–1 x) at x = `1/5` is ______.

Options

• `- (2sqrt(6))/5`

• `-2sqrt(6)`

• `-sqrt(6)/5`

• None

Answer 1

The value of cos (2cos^–1 x + sin^–1 x) at x = `1/5` is `underlinebb(- (2sqrt(6))/5)`.

Explanation:

cos [2cos^–1 x + sin^–1 x]

= cos [cos^–1 x + cos^–1 x + sin^–1 x]

= cos [cos^–1 x + π/2]

= –sin [cos^–1 x]

= `-sin [sin^-1 sqrt(1 - x^2)]`

= `-sqrt(1 - x^2)`

= `-sqrt(1 - (1/5)^2`

= `-sqrt(24/25)`

= `-(2sqrt(6))/5`