Question

How do you evaluate `cos[ 2sin^-1(5/13)]`?

Answer 1

The solution is `119/169` or 0.7041

Explanation:

Assume `sin^(-1)(5/13)=x`_(1)
`=>sinx=5/13`_____(2)
Therefore
`cos(2sin^(-1)(5/13))`=`cos2x` [since freom equation (1)]
`=1-2sin^2x`
`=1-2(5/13)^2`
`=119/169`

which is required solution.