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

#### 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

#### Video TutorialsVIEW ALL [5]

Solution Prove that (Sin Theta)/(1-cottheta) + (Cos Theta)/(1 - Tan Theta) = Cos Theta + Sin Theta Concept: Trigonometric Identities.
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