Question

if cosec theta + cot theta =1/3 then cosec theta - cot theta

Answer 1

this is easiest method

Answer 2

Solution:

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we know the Trigonometric identity:

cosec²A - cot²A = 1

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Here ,

It is given that,

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

Multiply both sides by

$\left(cosec\theta - cot\theta \right)$

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

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

$\implies 1=\left(cosec\theta - cot\theta \right) \times\frac{1}{3}$

$\implies 3=\left(cosec\theta - cot\theta \right)$

Therefore,

$\left(cosec\theta - cot\theta \right)=3$

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