Question

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

Options

• -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

sin²α + cos²α + sin²α = 3 sinα cosα

2 sin²α - 3sinα cos α + cos²α = 0

(2sinα - cos α)( sinα - cosα) = 0

⸫ cotα = 2 or cotα = 1