Question

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

Answer 1

Given the function below

`cot\theta=\cos\theta csc\theta`

Where

`csc\theta=(1)/(\sin\theta)`
`\begin{gathered} cot\theta=\cos\theta csc\theta \\ cot\theta=\cos\theta*(1)/(\sin) \\ cot\theta=(\cos\theta)/(\sin\theta) \end{gathered}`

Also recall that the contangent formula is

`cot\theta=(\cos\theta)/(\sin\theta)`

Thus;

`\begin{gathered} cot\theta=\cos\theta csc\theta \\ (\cos\theta)/(\sin\theta)=(\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