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Trigonometrical Equations
medium
The number of solutions of the pair of equations $ 2 \sin ^2 \theta-\cos 2 \theta=0 $, $ 2 \cos ^2 \theta-3 \sin \theta=0$ in the interval $[0,2 \pi]$ is
A
zero
B
one
C
two
D
four
(IIT-2007)
Solution
$ 2 \sin ^2 \theta-\cos 2 \theta=0 \Rightarrow \sin ^2 \theta=\frac{1}{4} $
$ \text { also } 2 \cos ^2 \theta=3 \sin \theta \Rightarrow \sin \theta=\frac{1}{2} $
$ \Rightarrow \text { two solutions in }[0,2 \pi]$.
Standard 11
Mathematics
