JEE PYQ: Trigonometric Equations And Inequations Question 14
Question 14 - 2019 (12 Apr Shift 1)
The number of solutions of the equation $1 + \sin^4 x = \cos^2 3x$, $x \in \left[-\frac{5\pi}{2}, \frac{5\pi}{2}\right]$ is:
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(1) 3
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(2) 5
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(3) 7
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(4) 4
Show Answer
Answer:
Solution
L.H.S. $\ge 1$ and R.H.S. $\le 1 \Rightarrow$ both equal 1.
$\sin x = 0$ and $\cos^2 x = 1 \Rightarrow x = 0, \pm\pi, \pm 2\pi$
Total solutions $= 5$.
BETA
