Question

How to solve this???​

Answer 1

Explanation:

`\large\sf{\sqrt{(1+sin\theta)/(1-sin\theta)}+\sqrt{(1-sin\theta)/(1+sin\theta)}}`

`\\`

`\large \sf{=(\left(√(1+sin\theta)\right)^(2)+\left(√(1-sin\theta)\right)^(2))/(√((1-sin\theta)(1+sin\theta)))}`

`\\`

`\large\sf{=\frac{1-sin\theta+1+sin\theta}{\sqrt{1^(2)-sin^(2)\theta}}}`

`\\`

`\large \sf{=\frac{2}{\sqrt{cos^(2)\theta}}}`

`\\`

`\large\sf{= (2)/(cos\theta)}`

`\\`

`\large\sf{= 2sec\theta}`

`\\`

`\large\sf{=RHS}`

Therefore,

`\large\sf\red{\sqrt{(1+sin\theta)/(1-sin\theta)}+\sqrt{(1-sin\theta)/(1+sin\theta)}=2sec\theta}`