Question
Download Solution PDFThe value of \(\rm \sqrt{{1 \ + \ \cos A} \over 1 \ - \ \cos A}\) is:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
\(\rm \sqrt{{1 \ + \ \cos A} \over 1 \ - \ \cos A}\)
Concept used:
sin2θ + cos2θ = 1
Calculation:
\(\rm \sqrt{{1 \ + \ \cos A} \over 1 \ - \ \cos A}\)
⇒ \(\rm \sqrt{{(1 \ + \ \cos A)(1 \ + \ \cos A)} \over (1 \ - \ \cos A)(1 \ + \ \cos A)}\)
⇒ \(\rm \sqrt{{(1 \ + \ \cos A)^2} \over 1 \ - \ \cos^2 A}\)
⇒ \(\rm \sqrt{{(1 \ + \ \cos A)^2} \over sin^2 A}\)
⇒ \(\rm\frac{1 \,+\, cosA}{sinA}\)
⇒ \(\rm\frac{1}{sinA} + \frac{cosA}{sinA}\)
⇒ cosec A + cot A
∴ The required answer is cosec A + cot A.
Last updated on Jul 12, 2025
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