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If the equation $k \cos x - 3 \sin x = k + 1$ has a solution for $x$ then

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0≤k≤8

k≥4

2k≤1

k≤4

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detailed solution

Correct option is D

If kcosx-3sinx=k+1 has a solution, then -k2+9≤k+1≤k2+9 ⇒k+1≤k2+9 ⇒k+12≤k2+9 ⇒k≤4

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If the equation kcosx−3sinx=k+1has a solution for x then

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If the equation $k \cos x - 3 \sin x = k + 1$ has a solution for $x$ then