Question

checking my answer

write the following in terms of cos and sin:

cot/sec

(cos)(sin)/cos

if not please break down what i should do

Answer 1

\[\frac{\cot(x)}{\sec(x)} \\ \\ = \frac{(\frac{\cos(x)}{\sin(x)})}{(\frac{1}{\cos(x)})} \\ \\ = \frac{(\frac{\cos(x)}{\sin(x)})}{(\frac{1}{\cos(x)})} \times \frac{cos(x)}{cos(x)} \\ \\ =\frac{\cos^2(x)}{\sin(x)} \\ \\ =\cos(x)\cot(x)\]
Firstly you should change the \(cot(x)\) to \(\frac{cos(x)}{sin(x)}\) and \(sec(x)\) to \(\frac{1}{cos(x)}\) with trig identities. Then, get rid of the \(\frac{1}{cos(x)}\) in the denominator by multiplying \(\frac{cos(x)}{cos(x)}\) and simplify.

Answer 2

Reminder: your final result MUST be written in terms of sin x and cos x alone. Please read through @.Sam. 's explanation and try to finish this problem by focusing on re-writing cot x in terms of sin x and cos x.