Question

Solve for x?

sin²x - 4 sin x + 3 = 0, 0  ≤ x ≤ \(π/2\)

1. \(π/6\)
2. \(π/4\)
3. \(π/2\)
4. \(π/3\)

Answer 1

Correct Answer - Option 3 : \(π/2\)

Given:

sin²x - 4 sin x + 3 = 0

Calculation:

Let sinx = k

⇒ k² - 4k + 3 = 0

⇒ k² - 3k - k + 3 = 0

⇒ k(k - 3) - 1(k - 3) = 0

⇒ (k - 1)(k - 3) = 0

k = 1 or k = 3

Then,

⇒ sin x = 1

⇒ x = sin ^-1(1)

∴ x = π/2