Question

find the value of (cosec2 theta-1)× tan2 theta

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Answer:

(cosec²$\theta$ - 1) * tan²$\theta$ = 1

Step-by-step explanation:

We need to find the value of (cosec²$\theta$ - 1) * tan²$\theta$

We know that sin²$\theta$ + cos²$\theta$ = 1

Dividing the above by sin²$\theta$

=> 1 + cot²$\theta$ = cosec²$\theta$

Therefore,

(cosec²$\theta$ - 1 ) * tan²$\theta$ = cot²$\theta$ * tan²$\theta$

We know that tan²$\theta$ = $\frac{1}{cot^2\theta}$

=> cot²$\theta$ * tan²$\theta$ = cot²$\theta$ *  $\frac{1}{cot^2\theta}$

                         = 1

Therefore, (cosec²$\theta$ - 1) * tan²$\theta$ = 1