Question

prove that sin theta.cos( 90°-theta)+cos theta sin theta(90°-theta)=1

Answer 1

Considering L.H.S-
sin theta.cos(90-theta)+cos theta.sin(90-theta)
=sin theta.sin theta+ cos theta. cos theta
{as sin(90-A)=cosA and cos(90-A)=sinA}
=sin^2theta+cos^2theta
=1
=RHS{sin2A+cos2A=1}
Hence proved..
hope it helpzzz u ☺️

Answer 2

Let theta be A
LHS
Sin A . Cos(90 - A) + Cos A . Sin ( 90 - A)
Sin A . Sin A + Cos A . Cos A
[Cos(90-A) = SinA]
[Sin(90-A) = CosA]
Sin^2A + Cos^2A
= 1 = RHS [using identity ]
Hence Proved.