Help needed with Cambridge Integration Question (1 Viewer)

[Half-Blood]

The question is attached- otherwise its Q49, p178 in cambridge- i remember that I solved it before but I can't remember how.
The "free" solutions from the guy with the Russian-sounding name didn't have it... so can someone with a complete set of solutions and/or is uber smart help me out?

Cheers, :wave:

 

[Mattamz]

first you need the subsitution
u=x - π/2
du = dx

and also to recognise that:
cosx = cos(u + π/2)
= cos(u)cos(π/2) - sin(u)sin(π/2)
= - sin(u)

then get you to first part, then since its odd and the intergral is between a and -a (in this case pi/2) its equal zero.

 

[Half-Blood]

Ty!