Question

Cosec theta + cot theta equals to K then prove that cos theta equals to K square minus 1 by K square + 1

Answer 1

here is your correct answer

Answer 2

given

$\cosec \theta + \cot \theta = k$

Now RHS

$\frac{ {k}^{2} - 1}{ {k}^{2} + 1} \\ \\ = \frac{( {cosec \theta + \cot \theta})^{2} - 1}{( {cosec \theta + cot \theta})^{2} + 1} \\ \\ = \frac{2 {cot}^{2} \theta + 2cosec \theta cot \theta}{2 {cosec}^{2} \theta + 2cosec \theta cot \theta }$

$= \frac{2cot \theta(cot \theta + cosec \theta)}{2coec \theta(cosec \theta + cot \theta)} \\ \\ = \frac{cot \theta}{cosec \theta} \\ \\ = cos \theta$