Question

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 =

Explanation:

Step1: Substitute trigonometric identities

Recall that \(\cot\theta=\frac{\cos\theta}{\sin\theta}\) and \(\sec\theta = \frac{1}{\cos\theta}\).
So, \(\cot\theta\sin\theta\sec\theta=\frac{\cos\theta}{\sin\theta}\times\sin\theta\times\frac{1}{\cos\theta}\)

Step2: Simplify the expression

Cancel out \(\sin\theta\) in the numerator and denominator of \(\frac{\cos\theta}{\sin\theta}\times\sin\theta\), we get \(\cos\theta\times\frac{1}{\cos\theta}\)
Then cancel out \(\cos\theta\), the result is \(1\)

Answer:

\(1\)