Question

Simplify the trigonometric expression sec theta cos theta a. tan theta b. 1 c. cot theta d. sin theta

Answer 1

Question:<u /> Simplify the trigonometric expression secӨcosӨ.

For each of the three basic trig functions, (sin, cos, tan) there are three more which act as their reciprocals. (csc, sec, and cot respectively)

Reciprocals, of course, are flipped fractions. If you have some number x, the reciprocal can be expressed as $\frac{1}x$.

An important property of reciprocals is that if you mutliply them together they will cancel out--take $\frac{4}7\times\frac{7}4$ for example.

Since secӨ is literally defined as the reciprocal of cosӨ, it is evident that
$\boxed{\sec\Theta\cos\Theta=1}$