Question

Prove that Sin(70+theta)-cos(20-theta)=0

Answer 1

Let cos(20-tetha) remain same..

Let us change Sin(70-tetha)

As we know that...
Sin(90-tetha)=Cos tetha
Sin(70-tetha)=Cos[90-(70+tetha)]
=Cos(20+tetha)

Cos(20-tetha) - Cos(20-tetha) = 0

Hence proved...

Answer 2

sin(70+Θ)-cos(20-Θ)=0
LHS
sin(70+Θ)-cos(20-Θ)
sin(70+Θ)-cos[90-(20-Θ)]              {complementary angles cos(90-Θ)=sinΘ}
sin(70+Θ)-cos(90-20+Θ)
sin(70+Θ)-sin(70+Θ)
0
Therefore LHS=RHS
So sin(70+Θ)-cos(20-Θ)=0