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Prove the Following Trigonometric Identities. Cos A/(1 - Tan A) + Sin A/(1 - Cot A) = Sin a + Cos a - CBSE Class 10 - Mathematics

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Question

Prove the following trigonometric identities.

`cos A/(1 - tan A) + sin A/(1 - cot A)  = sin A + cos A`

Solution

We need to prove `cos A/(1 - tan A) + sin A/(1 -  cot A) = sin A + cos `

Solving the L.H.S, we get

`cos A/(1 - tan A) + sin A/(1 - cot A) = cos A/(1 - sin A/cos A) = sin A/(1 - cos A/sin A)`

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

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

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

`= ((cos A + sin A)(cos A - sin A))/(coos A - sin A)`   [using `a^2 - b^2  = (a + b)(a -b)`]

= cos A + sin A

= RHS

Hence proved.

  Is there an error in this question or solution?

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Solution Prove the Following Trigonometric Identities. Cos A/(1 - Tan A) + Sin A/(1 - Cot A) = Sin a + Cos a Concept: Trigonometric Identities.
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