Question

ac{(csc x+1)(csc x-1)}{csc^2x}\\" alt="\frac{(csc x+1)(csc x-1)}{csc^2x}\\" align="absmiddle" class="latex-formula">

cscθ·cos^2θ+sinθ= cscθ

Answer 1

Step-by-step explanation:

$\frac{( \csc x+1)( \csc x-1)}{ \csc ^2x} = \frac{ { \csc }^{2} x - 1}{ \csc^{2} x} \\ = 1 - \sin^{2} x = \cos^{2} x \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

b. Since csc theta = 1/sin theta, we can multiply both sides by sin theta and you will end up with

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

which is an identity.