Question

√(cosec^2 A - 1) = cos A cosec A​

Answer 1

Answer:

Proof has been shown in the explanation part.

Step-by-step explanation:

√(cosec² A - 1) = √(cot² A)          { 1+cot²θ = cosec²θ => cosec²θ- 1 = cot²θ}

                       = cot A                {square root of cot²A is cotA }

                       = cos A/sin A        {cotθ = cosθ / sinθ }

                       = cos A cosec A  { sinθ = 1 / cosecθ }

Hence proved