Question

if cosec theta=root 3-cot theta is:
a) 2/root3
b) root 3/2
c) root 3
d) 1/root 3

Answer 1

Correct Question- if cosecθ = √3 - cotθ then find value of cosecθ or cotθ?


ATQ

cosecθ = √3 - cotθ

cosecθ + cotθ = √3 ...(1)

We know

cosec²θ - cot²θ = 1

(cosecθ + cotθ)(coseθ -cotθ) = 1

√3(cosecθ - cotθ) = 1

cosecθ - cotθ = 1/√3 ... (2)

Adding 1 and 2

2cosecθ = √3 + 1/√3 = (3 + 1)/√3 = 4/√3

cosecθ = 2/√3

Putting value of cosecθ = 2/√3 in equation 2 we get

cotθ = √3 - 2/√3 = (3 - 2)/√3

cotθ = 1/√3

Thus values of

cosecθ = 2/√3

cotθ = 1/√3