Question

question 2 (mandatory) (1 point)
the simplified form of \\( \cos q \tan q \sin q \\) is
a) \\( 1 - \cos ^ { 2 } \theta \\)
b) \\( \sin ^ { 2 } \theta \cos \theta \\)
c) \\( \sin \theta \\)
d) \\( \frac { \sin ^ { 2 } \theta } { \cos \theta } \\)

Explanation:

Step1: Substitute the formula for $\tan\theta$

We know that $\tan\theta=\frac{\sin\theta}{\cos\theta}$. So, $\cos\theta\tan\theta\sin\theta=\cos\theta\times\frac{\sin\theta}{\cos\theta}\times\sin\theta$.

Step2: Simplify the expression

Cancel out the $\cos\theta$ terms. We get $\sin\theta\times\sin\theta=\sin^{2}\theta$. Also, from the Pythagorean identity $\sin^{2}\theta = 1-\cos^{2}\theta$.

Answer:

A. $1 - \cos^{2}\theta$