Question

Prove that : tanθ – cotθ/sinθ cosθ = tan^2θ- cot^2θ​

Answer 1

Step-by-step explanation:

Now,

\cot \theta-\tan \thetacotθ−tanθ

=\dfrac{\cos \theta}{\sin \theta}-\dfrac{\sin \theta}{\cos \theta}=sinθcosθ−cosθsinθ

=\dfrac{\cos^2 \theta-\sin^2 \theta}{\cos \theta.\sin \theta}=cosθ.sinθcos2θ−sin2θ

=\dfrac{2\cos^2 \theta-1}{\sin \theta.\cos \theta}=sinθ.cosθ2cos2θ−1.   [Since 1-\sin^2 \theta=\cos^2 \theta1−sin2θ=cos2θ]