Question

Prove the following!​

Answer 1

$\Large{\underline{\underline{\mathfrak{\green{\bf{QUESTION}}}}}}$.

$\Large\underline{\bf{\:To\:Prove}}$

$\mapsto\pink{\sf{\:\dfrac{1-\sin \theta}{1+ \sin \theta}\:=\:(\sec \theta - \tan \theta)^2}}$

$\Large{\underline{\underline{\mathfrak{\orange{\bf{Prove}}}}}}$.

$\mapsto\pink{\sf{\:\dfrac{1-\sin \theta}{1+ \sin \theta}}}$

$\:\:\:\:\:\small\orange{\sf{\:( Multiply\:by\:1-\sin \theta \:numerator\:and\:denominator )}}$

$\mapsto\sf{\:\dfrac{(1-\sin \theta)(1-\sin \theta)}{(1-\sin \theta)(1+\sin \theta)}}$

$\mapsto\sf{\:\dfrac{(1+\sin^2 \theta-2\times\sin \theta)}{(1^2-\sin^2 \theta)}}$

$\:\:\:\:\:\small\orange{\sf{\:\left(1-\sin^2 \theta\:=\:\cos^2 \theta \right)}}$

$\mapsto\sf{\:\dfrac{(1+\sin^2 \theta-2\times\sin \theta)}{(\cos^2 \theta)}}$

$\mapsto\sf{\:\dfrac{1}{\cos^2 \theta}+\dfrac{\sin^2 \theta}{\cos^2 \theta}-2\times \dfrac{\sin \theta}{\cos^2 \theta}}$

$\:\:\:\:\:\small\orange{\sf{\:\left(\dfrac{1}{\cos^2 \theta}\:=\:\sec^2 \theta \right)}}$

$\:\:\:\:\:\small\orange{\sf{\:\left(\dfrac{\sin \theta}{\cos \theta}\:=\:\tan \theta \right)}}$

$\mapsto\sf{\:\sec^2 \theta+\tan^2 \theta-2\times\tan \theta\times\sec \theta}$

$\:\:\:\:\:\small\orange{\sf{\:\left[x^2 + y^2 - 2xy\:=\:(x-y)^2\right]}}$

$\mapsto\sf{\:(\sec \theta+\tan \theta)^2}$

= R.H.S.

That's proved.

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Answer 2

BCCI said that IPL could be held after monsoon.. :)