Question
Download Solution PDFIf Cosec θ + Cot θ = m, find the value of \(\rm\frac{m^{2}−1}{m^{2}+1}\).
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFIdentity used:
cosec2θ – cot2θ = 1
Calculation:
⇒ cosec θ + cot θ = m ---- (1)
⇒ (cosec θ - cot θ)(cosec θ + cot θ) = 1
⇒ (cosec θ - cot θ) =1/m
⇒ cosec θ - cot θ = 1/m ---- (2)
By adding (1) and (2), we'll get
2cosecθ = m + 1/m
cosecθ = (m2 + 1)/2m ...(3)
By subtracting (1) and (2), we'll get
2cotθ = m - 1/m ...(4)
cotθ = (m2 - 1)/2m
⇒ \(\rm\frac{m^{2}−1}{m^{2}+1}\)
Putting eq. (3) annd (4) in above expression:
⇒ 2mcotθ/2mcosecθ
⇒ cotθ/cosecθ
⇒ cosθ
The value is cosθ.
Last updated on Jul 16, 2025
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