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Mathematics

Prove the following identities :
$1 - \dfrac{\text{sin}^2 A}{\text{1 + cos A}} = \text{cos A}$

Trigonometric Identities

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Answer

By formula,

sin² A = 1 - cos² A

Solving L.H.S. of the equation :

$\Rightarrow 1 - \dfrac{1 - \text{cos}^2 A}{\text{1 + cos A}} \\[1em] \Rightarrow 1 - \dfrac{\text{(1 - cos A)(1 + cos A)}}{\text{1 + cos A}} \\[1em] \Rightarrow 1 - (\text{1 - cos A}) \\[1em] \Rightarrow 1 - 1 + \text{cos A} \\[1em] \Rightarrow \text{cos A}.$

Since, L.H.S. = R.H.S.

Hence, proved that $1 - \dfrac{\text{sin}^2 A}{\text{1 + cos A}} = \text{cos A}$ .

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Prove the following identities :
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