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Trigonometrical Equations
easy
જો $2{\cos ^2}x + 3\sin x - 3 = 0,\,\,0 \le x \le {180^o}$, તો $x =$
A
${30^o},{90^o},{150^o}$
B
${60^o},{120^o},{180^o}$
C
${0^o},{30^o},{150^o}$
D
${45^o},{90^o},{135^o}$
Solution
(a) $2 – 2{\sin ^2}x + 3\sin x – 3 = 0$
$ \Rightarrow $$(2\sin x – 1)\,(\sin x – 1) = 0$
$ \Rightarrow $ $\sin x = \frac{1}{2}$ or $\sin x = 1$
$ \Rightarrow $ $x = \frac{\pi }{6},\,\frac{{5\pi }}{6}$, $\frac{\pi }{2}$
$i.e.,$ $30^\circ ,{\rm{ 150}}^\circ {\rm{, 90}}^\circ $.
Standard 11
Mathematics
