The number of solutions of the pair of equations $2\sin^{2}{ heta - \cos{2 heta = 0}}$ and $2\cos^{2}{ heta - 3\sin{ heta = 0}}$ in the interval $\lbrack 0,\ 2\pi brack$ is

Question

The number of solutions of the pair of equations $2\sin^{2}{	heta - \cos{2	heta = 0}}$ and $2\cos^{2}{	heta - 3\sin{	heta = 0}}$ in the interval $\lbrack 0,\ 2\pibrack$ is

Dr. Abubacker · Accepted Answer

(c)
$2\sin^{2}{	heta - \cos{2	heta = 0\ \  \Rightarrow \ \sin^{2}{	heta = \frac{1}{4}\ \ \  \Rightarrow \ \sin{	heta = \pm \frac{1}{2}}}}}$ …(i)
Also, $2\cos^{2}{	heta = 3\sin{	heta\ \  \Rightarrow \ 2\sin^{2}{	heta + 3\sin{	heta - 2 = 0}}}}$
$\Rightarrow \ \ \sin{	heta = \frac{1}{2}}$ …(ii)
From Eqs. (i) and (ii), $\sin{	heta = \frac{1}{2}}$
Two solutions exist in $\lbrack 0,\ 2\pibrack$

Q. The number of solutions of the pair of equations $2\sin^{2}{\theta - \cos{2\theta = 0}}$ and $2\cos^{2}{\theta - 3\sin{\theta = 0}}$ in the interval $\lbrack 0,\ 2\pi\rbrack$ is

Explanation

Reviewed by Dr. Abubacker

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