Q.

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

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a

K<1

b

K>1

c

K<2

d

K>2

answer is D.

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Detailed Solution

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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