Q. 2 G5.0( 1 Vote )

Prove the following identities

secθ (1 – sinθ)(secθ + tanθ) = 1

Answer :

Consider LHS,


LHS = secθ (1 – sinθ) (secθ + tanθ)


secθ (1 – sinθ) (secθ + tanθ) = (secθ - ) (secθ + tanθ)


We know that = tanθ.


secθ (1 – sinθ) (secθ + tanθ) = (secθ – tanθ) (secθ + tanθ)


We know that (a + b) (a – b) = a2 – b2.


secθ (1 – sinθ) (secθ + tanθ) = sec2θ – tan2θ


We know that sec2θ – tan2θ = 1.


secθ (1 – sinθ) (secθ + tanθ) = 1 = RHS


Hence proved.


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