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

cos theta - sec theta / sin theta

We are asked to simplify cos theta - sec theta / sin theta in terms of sine and cosine. sec theta is the inverse function of cos theta. This results to the expression : (cos theta - 1/ cos theta)/sin theta ( cos^2 theta - 1) / sin thetafrom the trigonometric identity which is cos^2 theta + sin^2 theta = 1; 
-sin ^2 theta / sin theta this is equal hence to -sin theta.

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