Question

prove that (cosec theta -cot theta )^2 =1-cos theta / 1+cos theta​

Answer 1

Answer:

hope this answer of mine helps you

Answer 2

Answer:

$\left(cosec\theta-cot\theta\right)^{2}=\left(\frac{1-cos\theta}{1+cos\theta}\right)$

Step-by-step explanation:

$LHS= \left(cosec\theta-cot\theta\right)^{2}$

$=\left(\frac{1}{sin\theta}-\frac{cos\theta}{sin\theta}\right)^{2}$

$=\left(\frac{1-cos\theta}{sin\theta}\right)^{2}$

$=\frac{(1-cos\theta)^{2}}{sin^{2}\theta}$

$=\frac{(1-cos\theta)^{2}}{1-cos^{2}\theta}\\=\frac{(1-cos\theta)^{2}}{(1-cos\theta)(1+cos\theta)}\\=\left(\frac{1-cos\theta}{1+cos\theta}\right)\\=RHS$

Therefore,

$\left(cosec\theta-cot\theta\right)^{2}=\left(\frac{1-cos\theta}{1+cos\theta}\right)$

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