Simplifying Trig Functions

Question

Write the trigonometric expression in terms of sine and cosine, and then simplify.

sin theta - csc theta/ cos theta

Answer 1

sinT - cscT/cosT

=sinT- 1/sinTcosT

= sinT - 1/sin2T/2

= sinT - 2/sin2T

Answer 2

f = sin theta - csc theta/ cos theta

step 1: csc theta = 1/sin theta

f = sin theta - (1/ sin theta) / cos theta

f = sin theta - 1 / ( sin theta * cos theta)

This is an acceptable answer. however you can continue simplifying with the double angle identity

step 2 : sin 2theta = 2 sin theta cos theta

Or (1/2) sin 2theta = sin theta cos theta

Using this identity in f

f = sin theta - 2 / sin 2theta