A-value-of-satisfying-4cos-2-sin-2sin-2-3sin-is-1-9pi-10-2-pi-10-3-13pi-10-4-17pi-10-

Question Number 18092 by Tinkutara last updated on 15/Jul/17

A value of θ satisfying

{4 \cos}^{2} θ \sin θ - {2 \sin}^{2} θ = 3 \sin θ is

(1) \frac{9 π}{10}

(2) \frac{π}{10}

(3) - \frac{13 π}{10}

(4) - \frac{17 π}{10}

Answered by ajfour last updated on 15/Jul/17

(\sin θ) (4 \cos^{2} θ - 2 \sin θ - 3) = 0

\sin θ = 0, or

4 - 4 \sin^{2} θ - 2 \sin θ - 3 = 0

\sin^{2} θ + \frac{\sin θ}{2} = \frac{1}{4}

\Rightarrow {(\sin θ + \frac{1}{4})}^{2} = \frac{1}{4} + \frac{1}{16} = \frac{5}{16}

\sin θ = \frac{- 1 \pm \sqrt{5}}{4}

θ = \frac{π}{10}, - \frac{3 π}{10}, and so on . .

Among the options, (1) and (2) with

θ = \frac{π}{10}, \frac{9 π}{10} are the correct options .

Commented by Tinkutara last updated on 15/Jul/17

Thanks Sir!