If cosecθ - cotθ = p , then the value of \(\frac{p^2-1}{p^2 + 1

1.	If cosecθ - cotθ = p , then the value of \(\frac{p^2-1}{p^2 + 1}\) is1. cosθ 2. -cosθ 3. sinθ 4. -sinθ
Answer» 2. -cosθ = P = cosecθ - cotθ = \(\frac{sin\theta}{1+cos\theta}\) p²+ 1 cosec²θ + cot²θ - 2cosecθ cotθ = 2 cosec θ (cosecθ - cotθ) = \(\frac{2}{1+cos\theta}\) Now \(\frac{p^2-1}{p^2+1}=1-\frac{2}{p^2+1}=1-\) \(\cfrac{2}{\frac{2}{1+cos\theta}}\) = - cosθ

If cosecθ - cotθ = p , then the value of \(\frac{p^2-1}{p^2 + 1}\) is1. cosθ 2. -cosθ 3. sinθ 4. -sinθ

Answer»

2. -cosθ

= P = cosecθ - cotθ = \(\frac{sin\theta}{1+cos\theta}\)

p²+ 1 cosec²θ + cot²θ - 2cosecθ cotθ

= 2 cosec θ (cosecθ - cotθ)

= \(\frac{2}{1+cos\theta}\)

Now \(\frac{p^2-1}{p^2+1}=1-\frac{2}{p^2+1}=1-\) \(\cfrac{2}{\frac{2}{1+cos\theta}}\) = - cosθ

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If cosecθ - cotθ = p , then the value of \(\frac{p^2-1}{p^2 + 1}\) is1. cosθ 2. -cosθ 3. sinθ 4. -sinθ

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