please show stepsworking thanks Simplify Sin theta cosec the

please show steps/working thanks

Simplify Sin theta (cosec theta - sin theta) to a single trigonometric ratio.

Solution

sin theta ( cosec theta - sin theta )

cosec theta = 1/ sin theta

so we can write

sin theta ( 1 / sin theta - sin theta )

= sin theta ( 1 - sin^2 theta / sin theta )

= ( 1- sin^2 theta )

1 - sin^2 theta = cos^2 theta ( by trigonometric identity )

= cos^2 theta