Question

prove that sec A ( 1-sin A) (secA + tan A)=1​

Answer 1

Step-by-step explanation:

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Answer 2

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

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$\sf :\implies\:{\bold{ sec A ( 1 - Sin A) ( sec A+ tan A) = 1 }}$

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$\sf :\implies\:{\bold{ ( Sec A - SecA\times Sin A) ( sec A+ tan A) = 1 }}$

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

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$\sf :\implies\:{\bold{ ( Sec A - \dfrac{1}{CosA}\times Sin A) ( sec A+ tan A) = 1 }}$

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$\sf{\red{\boxed{\bold{\dfrac{SinA}{CosA} = Tan A}}}}$

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$\sf :\implies\:{\bold{ ( sec A - Tan A) ( sec A+ tan A) = 1 }}$

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

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$\sf :\implies\:{\bold{ sec^2A - Tan^2A = 1 }}$

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

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$\sf :\implies\:{\bold{ 1 = 1 }}$

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LHS = RHS

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀........Hence Proved