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If the function $f (x) = \frac{Ksin x + 2 \cos x}{\sin x + \cos x}$ is strictly increasing for all values of x, then

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K<1

K>1

K<2

K>2

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detailed solution

Correct option is D

Since f(x)=Ksin ⁡x+2cos ⁡xsin ⁡x+cos ⁡x is strictly increasing for all x,f′(x)>0 for all xor (K−2)sec2x(sin⁡x+cos⁡x)2>0 for all xor K−2>0 or K>2

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If the function f(x)=Ksin ⁡x+2cos ⁡xsin ⁡x+cos ⁡xis strictly increasing for all values of x, then

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If the function $f (x) = \frac{Ksin x + 2 \cos x}{\sin x + \cos x}$ is strictly increasing for all values of x, then