Q. 3 G4.1( 14 Votes )

# Prove the following identities.

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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