Question

cos theta. cos (90°-theta) - sin theta. sin (90°-theta)= 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

OR

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

Answer 2

$answer$

$\cos( \alpha ) = \sin( \alpha )$

Cos (90 - theta) = Sin theta

Sin ( 90 - theta = Cos theta

According to question

= Cos theta . Sin theta - Sin theta . Cos theta

$\cos(theta) \times \sin(theta) = 1$

= 1 - 1

= 0

I hope help you