Question

If 1 + sin²α = 3 sinα cosα, then values of cot α are ______.

पर्याय

• -1, 1

• 0, 1

• 1, 2

• -1, -1

Answer 1

If 1 + sin²α = 3 sinα cosα, then values of cot α are 1, 2.

Explanation:

1 + sin²α = 3 sinα cosα

Divide both sides by sin²α:

`1/(sin^2alpha) + 1 = 3 * (cosalpha)/(sinalpha) ⇒ csc^2alpha + 1 = 3 cotalpha`

Using identity csc²α = 1 + cot²α:

1 + cot²α + 1 = 3 cotα ⇒ cot²α − 3 cotα + 2 = 0

(cotα − 1)(cotα − 2) = 0

cotα = 1 or 2​