Question

tan theta + cot theta = 2.cosec 2 theta

Answer 1

I hope this helps you

Answer 2

Solution:

LHS = $tan\theta + cot\theta$

= $tan\theta+ \frac{1}{tan\theta}$

=$\frac{tan^{2}\theta+1}{tan\theta}$

= $\frac{sec^{2}\theta}{tan\theta}$

= $\frac{\frac{1}{cos^{2}\theta}}{\frac{sin\theta}{cos\theta}}$

After cancellation, we get

= $\frac{1}{sin\theta \cdot cos\theta}$

= $\frac{1}{sin\theta} \cdot\frac{1}{cos\theta}$

= $cosec\theta \cdot sec\theta$

= RHS

Therefore,

$tan\theta + cot\theta$

=$cosec\theta\cdot sec\theta$