Question

if cosec theta - cot theta =1/3.then find the value of cosec theeta + cot theeta

Answer 1

it will help you.............

Answer 2

Answer:

$cosec\theta-cot\theta=\frac{1}{3}$

$\implies (cosec\theta-cot\theta)(cosec\theta+cot\theta)\\=\frac{1}{3}(cosec\theta+cot\theta)$

$\implies (cosec^{2}\theta-cot^{2}\theta)\\=\frac{1}{3}(cosec\theta+cot\theta)$

$\implies 1=\frac{1}{3}(cosec\theta+cot\theta)$

$\boxed {cosec^{2}\theta-cot^{2}\theta = 1}$

$\implies 3 = cosec\theta+cot\theta$

Therefore,

$If \: cosec\theta-cot\theta=\frac{1}{3}\\then \: cosec\theta+cot\theta=3$

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