Question

Prove that $(co\sec \theta +\sin \theta )(co\sec \theta -\sin \theta )={\cot }^2\theta +{\cos }^2\theta$.

Answer 1

LHS$=(cosec\theta +\sin \theta )(cosec\theta -\sin \theta )$

$=cose{c}^2\theta -{\sin }^2\theta$

$=(1+{\cot }^2\theta )-(1-{\cos }^2\theta )$......(Using Trigonometric Identities)

$={\cot }^2\theta +{\cos }^2\theta$

$=RHS$

Hence proved