Question

Prove this math problem​

Answer 1

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Answer 2

Answer:

Hence proved.

Step-by-step explanation:

The expression is: $\sqrt{\frac{cosec\theta-1}{cosec\theta+1}}=\frac{1-sin\theta}{cos\theta}$

Solve as follows:

$\sqrt{\frac{cosec\theta-1}{cosec\theta+1}}=\sqrt{\frac{\frac{1}{sin\theta}-1}{\frac{1}{sin\theta}+1}}$

                $=\sqrt{\frac{1-sin\theta}{1+sin\theta}$

                $=\sqrt{\frac{1-sin\theta}{1+sin\theta}\times \frac{1-sin\theta}{1-sin\theta}}$

                $=\sqrt{\frac{(1-sin\theta)^{2}}{1-sin^{2}\theta}}$

                $=\sqrt{\frac{(1-sin\theta)^{2}}{cos^{2}\theta}}$

                $=\frac{1-sin\theta}{cos\theta}$

Hence proved.