Answer:

Given, the expression is √[(1 - cos²θ)sec²θ] = tanθ

We have to determine if the given relation is true or not.

By using trigonometric identities,

cos² A + sin² A = 1

sin² A = 1 - cos² A

So, 1 - cos²θ = sin²θ

Now, √[(1 - cos²θ)sec²θ] = √(sin²θ sec²θ)

= sinθ × secθ

We know that sec A = 1/cos A

= sin θ/cos θ

We know that tan A = sin A/cos A

= tan θ

Therefore, √[(1 - cos²θ)sec²θ] = tanθ

✦ Try This: √[(1 - sin²θ)cosec²θ] = cotθ

Given, √[(1 - sin²θ)cosec²θ] = cotθ

We have to determine if the given relation is true or not.

By using trigonometric identity,

cos² A = 1 - sin² A

√[(1 - sin²θ)cosec²θ] = √(cos²θcosec²θ)

= cosθ × cosecθ

We know cosec A = 1/sin A

= cosθ/sinθ

We know that cot A = cos A/sin A

= cotθ