Q. 2 G5.0( 1 Vote )

# Prove the following identitiessecθ (1 – sinθ)(secθ + tanθ) = 1

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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