Question

1/tan A + cot A = cos A sin A​

Answer 1

Answer:

expecting it as helpful......

Answer 2

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

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$\sf :\implies\:{\bold{ \dfrac{1}{tanA + cot A} = cos A Sin A }}$

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

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

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$\sf :\implies\:{\bold{ \dfrac{1}{\dfrac{SinA}{CosA} + \dfrac{CosA}{SinA}} = cos A Sin A }}$

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$\sf :\implies\:{\bold{ \dfrac{1}{\dfrac{sin^2A + cos^2A}{CosA. SinA} } = cos A Sin A }}$

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$\sf{\red{\boxed{\bold{Sin^2A + Cos^2A = 1 }}}}$

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$\sf :\implies\:{\bold{ \dfrac{1}{\dfrac{1}{CosA.SinA}} = cos A Sin A }}$

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$\sf :\implies\:{\bold{ 1 \div \dfrac{1}{CosA. SinA} = cos A Sin A }}$

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$\sf :\implies\:{\bold{ 1 \times CosA. SinA= cos A Sin A }}$

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$\sf :\implies\:{\bold{ CosA . Sin a = cos A Sin A }}$

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LHS = RHS

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀...... Hence Proved