Given the function f (x) = cosx minus cos (x + π in half), X belongs to R (1). Find the maximum value of F (x) (2) if f (a) = three quarters, find the value of sin2a

Given the function f (x) = cosx minus cos (x + π in half), X belongs to R (1). Find the maximum value of F (x) (2) if f (a) = three quarters, find the value of sin2a

f(x)=cosx-(-sinx)
=sinx+cosx
=√2(√2/2*sinx+√2/2cosx)
=√2(sinxcosπ/4+cosxsinπ/4)
=√2sin(x+π/4)
So the maximum value = √ 2
f(a)=sina+cosa=3/4
Square on both sides
sin²a+cos²a+2sinacosa=9/16
1+sin2a=9/16
sin2a=-7/16