Question

Prove following identities: $(1-co{s}^2\theta )cose{c}^2\theta =1$

Answer 1

L.H.S

$=(1-{\cos }^2\theta ){\csc }^2\theta$

We know that

$\sin \theta =\frac{1}{\csc \theta }$

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

Therefore,

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

$=1$

R.H.S

Hence, proved.