Question
Download Solution PDFWhat is the value of \(\rm \sqrt{\frac{1+\tan^2 \theta}{1+\cot ^2\theta}} \)?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Expression: √[(1 + tan²θ) / (1 + cot²θ)]
Formula used:
1 + tan²θ = sec²θ
1 + cot²θ = csc²θ
Calculation:
√[(1 + tan²θ) / (1 + cot²θ)]
⇒ √[(sec²θ) / (csc²θ)]
⇒ √[(1 / cos²θ) / (1 / sin²θ)]
⇒ √[(sin²θ / cos²θ)]
⇒ √(tan²θ) = tanθ
∴ Value = tanθ
Last updated on Jun 28, 2025
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