Question

Prove that => ( 1 + costheta - sin^2thata ) / ( sintheta( 1 + costheta ) ) = cottheta .


11th CBSE 2015 .

Answer 1

Hi!
Here's your answer>>>>
Solving LHS
1+cos theta -sin²theta
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sin theta(1+cos theta)

1+cos theta-(1- cos²theta) (using Identity sin²theta=1- costheta)
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sin theta(1+costheta )

1+costheta - 1+cos² theta
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sin theta(1+costheta)

costheta +cos²theta
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sin theta (1+cos theta)

Taking common value out of bracket

costheta(1+cos theta)
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sin theta(1+costheta)

cos theta ( COSTHETA÷SINTHETA=COTTHETA )
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sin theta

cot theta = cot theta
LHS=RHS
HENCE PROVED


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