Question

Use trigonometric identities cosec²X = 3cot X-1 ​

Answer 1

Explanation:

cosec²x = 1/sin²x = (sin²x+cos²x)/sin²x =1 + cos²x/sin²x = 1 + cot²x.

Therefore:

1+cot²x = 3cot x - 1

cot²x - 3 cot x + 2 = 0

let cot x = t

t²-3t+2=0

t²-2t-t+2=0

t(t-2)-(t-2)=0

(t-1)(t-2)=0

t1=1

t2=2

so:

cot x = 1 then x1 = π/4 + πk

cot x = 2 then x2 = arccot(2) + πk

k is an integral.