Q. 3 G4.1( 14 Votes )
Prove the following identities.
Answer :
Consider LHS,
LHS = 
Multiplying and dividing by sinθ + cosθ + 1,
⇒ 
= 
× 
We know that (a + b) (a – b) = a2 – b2.
⇒ 
= 
= 
We know that 1 – cos2θ = sin2θ and sin2θ + cos2θ = 1.
= 
= 
= 
= 
We know that 
= secθ and 
= tanθ.
⇒ 
= secθ + tanθ
Multiplying and dividing by secθ – tanθ,
⇒ 
= secθ + tanθ × 
= 
We know that sec2 – tan2θ = 1.
∴ 
=
= RHS
Hence proved.
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