Question

Prove that : cot θ – tan θ = 2cos2 θ -1/sin θ . cos θ .

Answer 1

Solution:(Instead of θ,I use A).

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Given:

To prove that:

           $cot A - tan A = \frac{2cosA^2-1}{sinAcosA}$

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Proof:

We know that,

$tan A = \frac{sin A}{cos A}$,

$cot A = \frac{cos A}{sin A}$


LHS = cot A - tan A

=> $\frac{cos A}{sin A} - \frac{sin A}{cos A}$

=> $\frac{cos^2A - sin^2A}{sinAcosA}$

We know that,

=> $sin^2 A + cos^2A =1$

=> $sin^2 A = 1 - cos^2A$

=> $- sin^2A = cos^2A - 1$

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Hence,

=> $\frac{cos^2A +(- sin^2A)}{sinAcosA}$

=> $\frac{cos^2A+ (cos^2A-1) }{sinA cosA}$

=> $\frac{2cos^2A - 1}{sinAcosA}$

=> RHS,

                 ∴ Hence proved

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                                     Hope it Helps!!

=> Mark as Brainliest,.

Answer 2

I have given the answer in a simple manner :)