JEE PYQ: Trigonometric Equations And Inequations Question 18
Question 18 - 2019 (12 Jan Shift 1)
If $\sin^4 \alpha + 4\cos^4 \beta + 2 = 4\sqrt{2} \sin \alpha \cos \beta$; $\alpha, \beta \in [0, \pi]$, then $\cos(\alpha + \beta) - \cos(\alpha - \beta)$ is equal to:
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(1) $0$
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(2) $-1$
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(3) $\sqrt{2}$
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(4) $-\sqrt{2}$
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Answer:
Solution
By AM–GM: $\sin^4\alpha = 1$, $\cos^4\beta = \frac{1}{4}$
$\alpha = \frac{\pi}{2}$, $\beta = \frac{\pi}{4}$
$\cos(\alpha+\beta) - \cos(\alpha-\beta) = -\sin\beta - \sin\beta = -2\sin\frac{\pi}{4} = -\sqrt{2}$
BETA
