Question

1/sec a + tan a = sec a - tan a

Answer 1

Heya mate
here is your answer

I hope this will help u...✌️✌️
thank u:-)

Answer 2

$\sf{\underline{\boxed{\purple{\large{\bold{Solution }}}}}}$

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$\sf :\implies\:{\bold{ \dfrac{1}{SecA + TanA} = Sec A - Tan A }}$

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• Rationalize the denominator

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$\sf :\implies\:{\bold{ \dfrac{1}{SecA + TanA} \times \dfrac{ Sec A - Tan A}{ Sec A - Tan A} = Sec A - Tan A }}$

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$\sf :\implies\:{\bold{ \dfrac{Sec A - Tan A}{(SecA + TanA) ( Sec A - Tan A)} = Sec A - Tan A }}$

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$\sf{\red{\boxed{\bold{( a- b ) ( a + b ) = a^2- b^2}}}}$

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$\sf :\implies\:{\bold{ \dfrac{ Sec A - Tan A}{Sec^2A - Tan^2A} = Sec A - Tan A }}$

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$\sf{\red{\boxed{\bold{Sec^2A - Tan^2A = 1 }}}}$

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$\sf :\implies\:{\bold{ \dfrac{Sec A - Tan A}{1} = Sec A - Tan A }}$

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$\sf :\implies\:{\bold{ SecA - TanA= Sec A - Tan A }}$

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LHS = RHS

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀.........Hence Proved