Question

Find the value of cos(2cos^-1x + sin^-1x) at x = 1/5, where 0 ≤ cos^-1x ≤ π and - π/2 ≤ sin^-1x ≤ π/2

Answer 1

Now, cos(2cos^-1x + sin^-1x) 

= cos(cos^-1x + sin^-1x + cos^-1x)

= cos(π/2 + cos^-1x)

= - sin(cos^-1x)

= - sin(sin^-1√(1 - x²))

= - √(1 - x²)

When x = 1/5, then the value of the given expression is - √(1 - 1/25) = -2√4/5