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Trigonometrical Equations
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Number of solutions of $5$ $cos^2 \theta -3 sin^2 \theta + 6 sin \theta cos \theta = 7$ in the interval $[0, 2 \pi] $ is :-
A
$2$
B
$4$
C
$0$
D
None of these
Solution
$5 \cos ^{2} \theta-3 \sin ^{2} \theta+6 \sin \theta \cos \theta=7$
$5\left(\frac{1+\cos 2 \theta}{2}\right)-3\left(\frac{1-\cos 2 \theta}{2}\right)+3 \sin 2 \theta=7$
$4 \cos 2 \theta+3 \sin 2 \theta=6$
but $4 \cos 2 \theta+3 \sin 2 \theta \leq \sqrt{4^{2}+3^{2}}=5$
$\therefore $ Solution does not exist.
Standard 11
Mathematics
