write the expression in terms of sine and cosine, and simplify so that no quotients appear in the final…

write the expression in terms of sine and cosine, and simplify so that no quotients appear in the final expression and all functions are of θ only. cot θ sin θ sec θ cot θ sin θ sec θ =

write the expression in terms of sine and cosine, and simplify so that no quotients appear in the final expression and all functions are of θ only. cot θ sin θ sec θ cot θ sin θ sec θ =

Answer

Explanation:

Step1: Rewrite cotangent and secant

Recall that $\cot\theta=\frac{\cos\theta}{\sin\theta}$ and $\sec\theta = \frac{1}{\cos\theta}$. So the original expression $\cot\theta\sin\theta\sec\theta$ becomes $\frac{\cos\theta}{\sin\theta}\times\sin\theta\times\frac{1}{\cos\theta}$.

Step2: Simplify the expression

Cancel out the common - terms. The $\sin\theta$ in the numerator and denominator of $\frac{\cos\theta}{\sin\theta}\times\sin\theta\times\frac{1}{\cos\theta}$ cancels out, and the $\cos\theta$ also cancels out. We get $\frac{\cos\theta\times\sin\theta\times1}{\sin\theta\times\cos\theta}=1$.

Answer:

$1$