Find the value of the following expression: ![image.png](https://res.cloudinary.com/aptidude/image/upload/v1746528740/aptidude_questions/lunxltacmknaodc1bosk.png)

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Accepted Answer

Let's simplify the given expression step by step:

Expression: √(1 + sinθ) / √(1 - sinθ)

Step 1: Combine under a single square root:
= √[(1 + sinθ)/(1 - sinθ)]

Step 2: Multiply numerator and denominator by (1 + sinθ) to rationalize the denominator:
= √[(1 + sinθ)/(1 - sinθ)] × [(1 + sinθ)/(1 + sinθ)]
= √[(1 + sinθ)^2 / (1 - sin^2θ)]

Step 3: Recall that 1 - sin^2θ = cos^2θ:
= √[(1 + sinθ)^2 / cos^2θ]
= (1 + sinθ)/cosθ

Step 4: Express in terms of secθ and tanθ:
= 1/cosθ + sinθ/cosθ
= secθ + tanθ

Therefore, the value of the given expression is secθ + tanθ.

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