Question

Simplify
sin(theta)* sec^2(90-theta)

Answer 1

first, you will need to recall the identities,, some useful identities that will be applied here are:
(a) 1/sec(theta)=cos(theta) ; and
(b) cos(90-theta)=sin(theta)

,first, use identity (a) to change sec^2(90-theta) to 1/cos^2(90-theta),,
,then, use identity (b) to rewrite the latter term to 1/sin^2(theta)
,lastly, sin(theta) will be canceled, yielding:
1/sin(theta) or csc(theta)

:)