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If cosec theta - cot theta = 1/3 then find the value of ( cosec theta + cot theta)

cosec θ - cot θ = 1 / 3  (given)

now, cosec2 θ - cot2θ = 1

 ⇒ (cosec θ - cot θ) (cosec θ + cot θ) = 1

 ⇒ (cosec θ + cot θ) × 1 / 3 = 1

 ⇒ (cosec θ + cot θ) = 3

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Using the identity:-

cosec2 A cot2A= 1

We get that.....

(cosecA cotA)(cosec A+cot A)= 1

It is given that cosec A - cot A = 1/3, therefore we replace its value........

1/3 x (cosecA+ cotA) = 1

cosecA+ cotA= 1*3/1

cosecA+ cotA= 3.

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