Question

Verify the basic identity. What is the domain of validity?cot theta = cos theta csc thetasee image

Answer 1

Solution

Given the function below

$cot\theta=\cos\theta csc\theta$

Where

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

Also recall that the contangent formula is

$cot\theta=\frac{\cos\theta}{\sin\theta}$

Thus;

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

From the above deduction,

sinθ is the denominator,

Hence, the domain of validity is defined for the set of real numbers except for sinθ = 0