Question

If cosec theta +cot theta =1/5, find "cos theta" and determine the quadrant in which theta lies. The answer is (-12/13) in second quadrant ​

Answer 1

Solution :-

Provided :-

• cosec∅ + cot∅ = 1/5 ....(i)

We know :-

• cosec²∅ - cot²∅ = 1

From this :-

→ (cosec∅ + cot∅)(cosec∅ - cot∅) = 1

→ 1/5 (cosec∅ - cot∅) = 1

→ cosec∅ - cot∅ = 5 ....(ii)

Add (i) and (ii)

→ 2 cosec∅ = 26/5

→ cosec∅ = 13/5

→ sin∅ = 5/13

By putting in it (i) we get

→ cot∅ = - 12/5

→ tan∅ = -5/12

Now as sin is positive and tan is negetive

→ cos is negative

→ Second quadrant.

Value of cos∅

→ cos²∅ + sin²∅ = 1

→ cos²∅ = 1 - sin²∅

→ cos²∅ = 1 - 25/169

→ cos²∅ = 144/169

→ cos∅ = -12/13