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Prove that `(Sin Theta)/(1-cottheta) + (Cos Theta)/(1 - Tan Theta) = Cos Theta + Sin Theta` - ICSE Class 10 - Mathematics

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Question

Prove that `(sin theta)/(1-cottheta) + (cos theta)/(1 - tan theta) = cos theta + sin theta`

Solution

L.H.S = `(sin theta)/(1 - cot theta) + (cos theta)/(1- tan theta)`

`= (sin theta)/(1 - cos theta/sin theta) + cos theta/(1 - sin theta/cos theta)`

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

`= (sin^2 theta)/(sin theta - cos theta) - cos^2 theta/(sin theta - costheta)`

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

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

`= sin theta + cos theta`

= R.H.S

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APPEARS IN

 2014-2015 (March) (with solutions)
Question 7.3 | 4.00 marks
Solution Prove that `(Sin Theta)/(1-cottheta) + (Cos Theta)/(1 - Tan Theta) = Cos Theta + Sin Theta` Concept: Trigonometric Identities.
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