Question

Number of values of x which satisfy then relation `12tan^2x + 24/sqrt(3)tanx + 12sin^2x - 12sinx + 7` in (–2π, 4π) ______.

पर्याय

• 0.00

• 1.00

• 2.00

• 3.00

Answer 1

Number of values of x which satisfy then relation `12tan^2x + 24/sqrt(3)tanx + 12sin^2x - 12sinx + 7` in (–2π, 4π) 3.00.

Explanation:

`12tan^2x + 24/sqrt(3)tanx + 12sin^2x - 12sinx + 7` = 0

⇒ `12(tan^2x + 2 1/sqrt(3) tanx) + 12(sin^2x - sinx) + 7` = 0

`12[(tanx + 1/sqrt(3))^2 - 1/3] + 12(sin^2x - 2 1/2sinx + 1/4 - 1/4) + 7` = 0

`12(tanx + 1/sqrt(3))^2 -4 + 12(sinx - 1/2)^2 - 3 + 7` = 0

⇒ `(tanx + 1/sqrt(3))^2 + (sinx - 1/2)^2` = 0

∴ tanx = `-1/sqrt(3)` and sinx = `1/2`

x = `(5π)/6`

Number of solutions in (–2π, 4π) = 3