Question

cosec theta+cot theta = 1/3, find sin theta

Answer 1

Given that cosec∅ + cot∅ = 1/3......(1)

To find: sin∅

We know that,

cosec²∅ - cot²∅ = 1

→(cosec∅ + cot∅)(cosec∅ - cot∅) =1

→(cosec∅ - cot∅)/3 = 1 [From (1)]

→cosec∅ - cot∅ = 3..........(2)

Adding equations (1) and (2),we get:

2cosec∅ = 10/3

→cosec∅ = 5/3

We know that,

cosec∅ = 1/sin∅

→sin∅ = 3/5