# Prove that Sqrt((1 - Sin θ)/(1 + Sin θ)) = Sec θ - Tan θ - Mathematics

Sum

Prove that sqrt((1 - sin θ)/(1 + sin θ)) = sec θ - tan θ.

#### Solution

L.H.S. = sqrt(((1 - sin θ)(1 - sin θ))/((1 + sin θ)(1 - sin θ)))

= sqrt((1 + sin^2θ - 2sinθ)/(1 - sin^2θ)

= sqrt((1 + sin^2θ - 2sinθ)/(cos^2θ)

= sqrt( 1/cos^2θ + sin^2θ/cos^2θ - (2sin θ)/cos θ xx 1/cosθ

= sqrt( sec^2θ + tan^2 θ - 2 tan θ. sec θ)

= sqrt((sec θ - tan θ)^2)

= sec θ - tan θ
= R.H.S.
Hence proved.

Concept: Trigonometric Identities
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#### APPEARS IN

ICSE Class 10 Mathematics
Chapter 18 Trigonometry
Exercise | Q 6
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