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Addition and Subtraction of a Matrix

Prove the fol...

Question

Prove the following identity:
ii. $\frac{1}{(sin A + cos A)} + \frac{1}{(sin A - c o s A)} = \frac{2 sin A}{(1 - 2 {cos}^{2} A)}$

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Solution

Proving LHS $=$ RHS.

First we consider Left Hand Side (LHS),

$= \frac{1}{(sin A + cos A)} + \frac{1}{(sin A - cos A)}$

By taking LCM we get,

$= \frac{(sin A - cos A + sin A + cos A)}{({sin}^{2} A - {cos}^{2} A)}$

$= \frac{2 sin A}{(1 - {cos}^{2} A - {cos}^{2} A)}$

$= \frac{2 sin A}{(1 - 2 {cos}^{2} A)}$ .

Then, Right Hand Side $= \frac{2 sin A}{(1 - 2 {cos}^{2} A)}$ .

Therefore, LHS = RHS.

Hence proved.

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Addition and Subtraction of a Matrix

Standard XII Mathematics

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