Question

$secA(1 - \sin^{2} ) = cosa$
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Answer 1

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$\sf{\underline{\huge{\boxed{\bold{LHS}}}}}$

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$: \implies\: \sf{\bold{ SecA ( 1 - SinA) }}$

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$\sf{\red{\boxed{\bold{Sec A = \dfrac{1}{CosA}}}}}$

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$: \implies\: \sf{\bold{ \dfrac{1}{CosA} ( 1 - Sin^2A) }}$

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$\sf{\red{\boxed{\bold{1 - Sin^2\theta = cos^2 \theta}}}}$

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$: \implies\: \sf{\bold{\dfrac{1}{cosA}\times cos^2A }}$

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$: \implies\: \sf{\bold{\dfrac{1}{cosA}\times cosA\times cosA }}$

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$: \implies\: \sf{\bold{\dfrac{1}{cosA}\times cosA \times \cancel{CosA} }}$

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$: \implies\: \sf{\bold{CosA }}$

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$\sf{\underline{\huge{\boxed{\bold{RHS}}}}}$

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$: \implies\: \sf{\bold{cosA}}$

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$\sf{\underline{\huge{\boxed{\bold{Compare}}}}}$

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$\sf{\bold{CosA = Cos A}}$

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀....Hence Proved

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