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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