Question

Write the trigonometric expression in terms of sine and cosine, and then simplify. Csc theta - sin theta/sin theta_______

Answer 1

To write the trigonometric expression in terms of sine and cosine and then simplify, we substitute the values of csc theta and sin theta in terms of sine and cosine. The simplified expression is (1 - sin theta)/sin theta.

Step-by-step explanation:

To write the trigonometric expression in terms of sine and cosine and then simplify, we will first rewrite csc theta and sin theta in terms of sine and cosine.

csc theta = 1/sin theta

sin theta = sin theta

Now, substituting these values into the expression csc theta - sin theta/sin theta, we get:

csc theta - sin theta/sin theta = 1/sin theta - sin theta/sin theta = (1 - sin theta)/sin theta

This is the simplified expression in terms of sine and cosine.