Question

if cosec theta =41/40 then find the values of sin theta and sec theta.

Answer 1

Cosec θ = 41 / 40

Sin θ = 1 / cosec θ

Sin θ = 1 / 41 / 40

Sin θ = 40 / 41.

By using identity,

Sin ² θ + cos² θ = 1.

( 40 / 41 )² + cos² θ = 1.

cos² θ = 1 - 1600 / 1681

cos² θ = 1681 - 1600 / 1681

cos² θ = 81 / 1681

cos θ = √ 81 / 1681

Cos θ = 9 / 41

Cos θ = 1 / sec θ

Sec θ = 1 / Cos θ

Sec θ = 1 / 9 / 41

Sec θ = 41 / 9.