Question

Sec theta + cos theta /sec theta - cos theta= 3/5. Find the value of cosec theta.

Answer 1

(sec θ + cos θ) / (sec θ - cos θ) = 3/5

[(1/cos θ) + cos θ] / [(1/cos θ) - cos θ] = 3/5

[(1 + cos^2θ)/cos θ] / [(1 - cos^θ)/cos θ] = 3/5

(1 + cos^2θ) / (1 - cos^2θ) = 3/5

(1 + 1 - sin^2θ) / sin^2θ = 3/5

(2 - sin^2θ) / sin^2θ = 3/5

5(2 - sin^2θ) = 3sin^2θ

10 - 5sin^2θ = 3sin^2θ

10 = 8sin^2θ

sin^2θ = 10/8

sin^2θ = 5/4

1/sin^2θ = 4/5

cosec^2θ = 4/5 = 0.8

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Answer 2

Step-by-step explanation:

secx + cosx / secx - cosx = 3/5

(1/cosx + cosx)/(1/cosx - cosx) = 3/5

(1 + cos²x )/(1 - cos²x) = 3/5

(1 + cos²x) / sin²x = 3/5

(cosec²x + cot²x ) = 3/5

2cosec²x - 1 = 3/5

2cosec²x = 8/5

cosec²x = 4/5

cosecx = 2/5½