Question

Prove that cotA-tanA=2cos^A-1÷sinAcosA

Answer 1

your answer is in attachment .
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Answer 2

Hey!

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cot A - tan A = 2 cos²A - 1 / sin A cos A

L.H.S

cot A - tan A

(cos A / sin A) - (sin A / cos A)

cos²A - sin² A / cos A sin A

We know,
cos²A + sin²A = 1
sin²A = 1 - cos²A


So,

cos²A - ( 1 - cos²A) / cos A sin A

cos²A - 1 + cos²A / cos A sin A

= 2 cos²A - 1 / cos A sin A

L.H.S = R.H.S
Proved.


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