Question

The equation 3sin²x + 10 cos x – 6 = 0 is satisfied, if ______.

Options

• x = `"n"pi +- cos^-1 (1/3)`

• x = `2"n"pi +- cos^-1 (1/3)`

• x = `"n"pi +- cos^-1 (1/6)`

• x = `2"n"pi +- cos^-1 (1/6)`

Answer 1

The equation 3sin²x + 10 cos x – 6 = 0 is satisfied, if x = `2"n"pi +- cos^-1 (1/3)`.

Explanation:

3sin²x + 10 cos x – 6 = 0

⇒ 3 (1 – cos²x) + 10 cos x – 6 = 0

⇒ 3 cos²x – 10 cos x + 3 = 0

⇒ 3 cos²x – 9 cos x – cos x + 3 = 0

⇒ 3 cos x (cos x – 3) – 1 (cos x – 3) = 0

⇒ (cos x - 3) (3 cos x – 1) = 0

⇒ cos x = 3, (which is not possible)

or cos x = `1/3`

⇒ cos x = `1/3 = cos alpha`  .....(say)

⇒ x = `2"n"pi +- alpha`

⇒ x = `2"n"pi +- cos^-1 (1/3)`