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) = a^{2} – b^{2}.

⇒ =

=

We know that 1 – cos^{2}θ = sin^{2}θ and sin^{2}θ + cos^{2}θ = 1.

=

=

=

=

We know that = secθ and = tanθ.

⇒ = secθ + tanθ

Multiplying and dividing by secθ – tanθ,

⇒ = secθ + tanθ ×

=

We know that sec^{2} – tan^{2}θ = 1.

∴ = = RHS

Hence proved.

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