Question

P=cosx - sinx, q=1-sin 3 x/1-sinx, r=1+cos 3 x/1+cosx , what is the value of p+q-r

Answer 1

p=cosx-sinx
q=1-sin³x/1-sinx
=(1-sinx)(1+sinx+sin²x)/(1-sinx)
=1+sinx+sin²x
r=1+cos³x/1+cosx
=(1+cosx)(1-cosx+cos²x)/(1+cosx)
=1-cosx+cos²x
∴, p+q-r
=cosx-sinx+1+sinx+sin²x-(1-cosx+cos²x)
=cosx+1+sin²x-1+cosx-cos²x
=sin²x-cos²x+2cosx
=1-cos²x-cos²x+2cosx [∵, sin²x+cos²x=1]
=1+2cosx-2cos²x