Find the exact value of the given expression sin2 cos135Solu

Find the exact value of the given expression. sin^2 cos-1(3/5))

Solution

sin(2 cos^-1(3/5))

let us say cos^-1(3/5) = x , then our problem becomes sin(2x)

3/5=cos(x)

identity sin^2(x) +cos^2(x) =1

sin^2(x) +(3/5)^2 =1

sin^2(x) = 1-9/25

sin^2(x) = 16/25

sinx = 4/5

now sin(2x) = 2sinx.cosx

= 2(4/5).(3/5)

= 24/25

the value of the given expression is 24/24