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Please help me give me good answer i will mark brainlist​

Answer»

GIVEN:

\sf{\dfrac{1- sin \theta }{cos \theta} + \dfrac{cos \theta }{1- sin \theta} = 2 sec \theta}

TO FIND:

Evaluate

SOLUTION:

Take L.H.S.

\rm{\longrightarrow \dfrac{1- sin \theta }{cos \theta} + \dfrac{cos \theta }{1- sin \theta} }

\rm{\longrightarrow \dfrac{(1-sin \theta)^2 + cos^2 \theta}{cos \theta (1- sin \theta)} }

Using IDENTITY

(a–b)² = a² –2ab + b²

\rm{\longrightarrow \dfrac{1 - 2sin \theta + sin^2 \theta + cos^2 \theta }{cos \theta (1- sin \theta)}}

Using TRIGONOMETRIC Identity

sin²θ + cos²θ = 1

\rm{\longrightarrow \dfrac{1+ 1 - 2 sin \theta}{cos \theta (1- sin \theta)}}

\rm{\longrightarrow \dfrac{2 - 2 sin \theta}{cos \theta (1- sin \theta)} }

\rm{\longrightarrow \dfrac{2 \cancel{(1- sin \theta)}}{cos \theta \cancel{(1- sin \theta)}}}

\rm{\longrightarrow \dfrac{2}{cos \theta}}

We KNOW that, 1/cosθ = secθ

\bf{\longrightarrow 2 sec \theta = R.H.S.}

\Large{\underline{\underline{\bf{Hence \: Proved \text{!}}}}}

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