Question

find the value of cos theta cos(90-theta )-sin theta sin (90-theta)ans 0

Answer 1

Using identities cos(90-x) = sinx and sin(90-x) = cosx

cosx.cos(90-x) - sinx.sin(90-x)
= cosxsinx - sinxcosx
= 0

Answer 2

cosβ*cos(90-β)-sinβsin(90-β)=0
we know that 
    cos(90-β)=sinβ and sin(90-β)=cosβ
therefore,
cosβ*cos(90-β)-sinβ*sin(90-β)
= cosβ*sinβ-sinβ*cosβ
=0
hence proved