1) f (x) = sinx+sin (x+pai/2) = sinx+cosx = radical number 2[ (radical number 2/2)sinx+ (radical number 2/2)cosx]= radical number 2 [sinxcos (pai/4)+cosxsin (.

2) Because f(x)= radical 2sin[x+ (pai /4)], the range of f(x) is [-radical 2, radical 2], that is, the maximum and minimum values of f(x) are radical 2 and negative radical 2 respectively.

3)f(a)=3/4, and substitute it into the original function f(x)=sinx+sin(x+ derivative /2).

F(a)= Sina +sin(a+Pai/2)= Sina +cosa=3/4.

Sina +cosa=3/4 left and right squares.

Sina Square +2 Sinakosa+Kossa Square =9/ 16

That is 1+sin2a=9/ 16.

sin2a=-7/32