Question

simplify the trig expression csc θ cot θ——————sec θ

Answer 1

To simplify:

$\frac{\csc\theta\cot\theta}{\sec\theta}$

We know that,

$\begin{gathered} \csc \theta=\frac{1}{\sin\theta} \\ \cot \theta=\frac{\cos\theta}{\sin\theta} \\ \sec \theta=\frac{1}{\cos \theta} \end{gathered}$

Using this we get,

$\begin{gathered} \frac{\csc\theta\cot\theta}{\sec\theta}=\frac{\frac{1}{\sin\theta}\cdot\frac{\cos\theta}{\sin\theta}}{\frac{1}{\cos\theta}} \\ =\frac{1}{\sin\theta}\cdot\frac{\cos\theta}{\sin\theta}\times\frac{\cos\theta}{1} \\ =\frac{\cos^2\theta}{\sin^2\theta} \\ =(\frac{\cos \theta}{\sin \theta})^2 \\ =\cot ^2\theta \end{gathered}$

Hence, the answer is,

$\cot ^2\theta$