# (1+sinA))(1-sinA)=1/sec^2A prove that?

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#### Explanation

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#### Explanation:

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Øko Share
Feb 9, 2018

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#### Explanation:

We want to verify the identity

$\left(1 + \sin \left(a\right)\right) \left(1 - \sin \left(a\right)\right) = \frac{1}{\sec} ^ 2 \left(a\right)$

We will use

• ${\cos}^{2} \left(x\right) = 1 - {\sin}^{2} \left(a\right)$
• $\cos \left(x\right) = \frac{1}{\frac{1}{\cos} \left(x\right)} = \frac{1}{\sec} \left(x\right)$

$L H S = \left(1 + \sin \left(a\right)\right) \left(1 - \sin \left(a\right)\right)$

$= 1 - {\sin}^{2} \left(a\right)$

$= {\cos}^{2} \left(a\right)$

$= \frac{1}{\sec} ^ 2 \left(a\right) = R H S$

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