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Prove the Following Trigonometric Identities. Cos a Cosec a - Sin a Sec A)/(Cos a + Sin A) = Cosec a - Sec a - CBSE Class 10 - Mathematics

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Question

Prove the following trigonometric identities.

`(cos A cosec A - sin A sec A)/(cos A + sin A) = cosec A - sec A`

Solution

We have to prove `(cos A cosec A - sin A sec A)/(cos A + sin A) = cosec A - sec A`

So,

`(cos A cosec A - sin A sec A)/(cos A + sin A) = (cos A 1/sin A - sin A 1/cos A)/(cos A + sin A)`

`= ((cos^2 A - sin^2 A)/(sin A cos A))/(cos A + sin A)`

`= (cos^2 A - sin^2 A)/(sin A cos A(cos A + sin A))`

`= ((cos A - sin A)(cos A + sin A))/(sin A cos A(cos A + sin A))`

`= (cos A - sin A)/(sin A cos A)`

`= cos A/(sin A cos A) - sin A/(sin A  cos A)``

`= 1/sin A - 1/cos A``

`= cosec A - sec A`

Hence proved.

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Solution Prove the Following Trigonometric Identities. Cos a Cosec a - Sin a Sec A)/(Cos a + Sin A) = Cosec a - Sec a Concept: Trigonometric Identities.
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