Practicing Success
The value of x, if 2 sin2 x = 2 - 3 sin x, is : |
$\frac{\pi}{6}$ $\frac{\pi}{4}$ $\frac{\pi}{2}$ $\frac{\pi}{3}$ |
$\frac{\pi}{6}$ |
2 sin2 x = 2 - 3 sin x 2 sin2 x + 3 sin x - 2 = 0 2 sin2 x + 4 sin x - sinx - 2 = 0 2sinx ( sinx + 2 ) -1( sinx + 2 ) = 0 ( 2sinx -1 )(sinx + 2 ) = 0 Either ( 2 sinx - 1 = 0 ) OR ( sinx + 2 = 0 ) { sinx + 2 = 0 is not possible } So, 2 sinx - 1 = 0 sinx = \(\frac{1 }{2}\) { we know, sin30º = \(\frac{1 }{2}\) } So, x = 30º = \(\frac{π}{6}\) |