Question

Simplify csc θ(1−cos^2 θ)/sinθ cos θ to a single trigonometric function

Answer 1

Answer:

$\frac{cosec\alpha(1-cosx^{2} \alpha ) }{sin\alpha cos\alpha } = sec\alpha$

Step-by-step explanation:

Step(i):-

Given that the trigonometric function

            $\frac{cosec\alpha(1-cosx^{2} \alpha ) }{sin\alpha cos\alpha }$

  we know that    sin²∝ + cos²∝ = 1

                      ⇒    sin²∝ = 1- cos²∝

Now we have to simplify the given trigonometric function

                =       $\frac{cosec\alpha(sin^{2} \alpha ) }{sin\alpha cos\alpha }$

               =       $\frac{cosec\alpha(sin \alpha ) }{ cos\alpha }$

Step(ii)

         we know that  cosec∝ = 1/ sin∝

              = $\frac{\frac{1}{sin\alpha } (sin \alpha ) }{ cos\alpha }$

    After cancellation sine function, we get

          =  $\frac{1 }{ cos\alpha } = sec\alpha$

Final answer:-

$\frac{cosec\alpha(1-cosx^{2} \alpha ) }{sin\alpha cos\alpha } = sec\alpha$