Question

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

Answer 1

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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Hope it helps...!!!

Answer 2

HEY

HERE IS ANSWER.

TO PROVE:

cotA-tanA= 2 cos^2A-1/sinA*cosA

LHS

$\frac{cos \: a}{sin \: a} - \frac{sin \: a}{cos \: a}$

(since
cot= cos /sin

tan=sin/cos)

take LCM

$\frac{cos^{2} a - sin^{2}a }{sin \: a \times \: cos \: a}$
we know that

sin^2A=1-cos^2A

so

$\frac{cos ^{2} a - 1 + cos^{2} a}{sin \: a \times cos \: a}$

hence

$\bf{ \frac{2cos^{2} a - 1 }{sin \: a \times cos \: a}}$
LHS=RHS

HOPE IT HELPS

THANKS