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[JEE Advanced 2002] the number of integral values of k for which 7 cos x 5 sin

VAVidaara Admin Asked 2d ago 0 views 1 answer
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The number of integral values of $k$ for which $7\cos x+5\sin x=2k+1$ has a solution is

(a) $4$
(b) $8$
(c) $10$
(d) $12$

1 Answer

VAVidaara Admin ✓ Vidaara Team ✓ Accepted · 2d ago ▲ 0

Correct answer: (b) $8$

$7\cos x+5\sin x\in[-\sqrt{74},\sqrt{74}]\approx[-8.6,8.6]$, so $-8.6\le2k+1\le8.6\Rightarrow k\in\{-4,\dots,3\}$ — $8$ integers.

JEE Advanced 2002 · Trigonometry — verified solution by the Vidaara Team.

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