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cot{A}{2}-tan{A}{2} will be equal to

Question

$co t \frac{A}{2} - t an \frac{A}{2}$ will be equal to

A

t an A

B

co t

C

2 co t

D

2 t an A

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co t \frac{A}{2} - t an \frac{A}{2}

will be equal to

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Text solutionVerified

cot \frac{A}{2} - tan \frac{A}{2}

\Rightarrow \frac{cos \frac{A}{2}}{sin \frac{A}{2}} - \frac{sin \frac{A}{2}}{cos \frac{A}{2}} = \frac{cos ^{2} \frac{A}{2} - sin ^{2} \frac{A}{2}}{sin \frac{A}{2} cos \frac{A}{2}}

\Rightarrow \frac{cos A}{sin \frac{A}{2} cos \frac{A}{2}} [∵ cos^{2} \frac{θ}{2} - sin^{2} \frac{θ}{2} = cos θ]

Multiply and divide by

2,

we get

\Rightarrow \frac{2 cos A}{2 sin \frac{A}{2} cos \frac{A}{2}} = \frac{2 cos A}{sin A} [∵ 2 sin \frac{θ}{2} cos \frac{θ}{2} = sin θ]

= 2 cot A

Hence, the answer is

2 cot A .

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Question Text	$co t \frac{A}{2} - t an \frac{A}{2}$ will be equal to
Answer Type	Text solution:1
Upvotes	150