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Question: If the function f(x) = \(\frac{a\sin x + 2\cos x}{\sin x + \cos x}\)is increases for all values of x...

If the function f(x) = asin⁡x+2cos⁡xsin⁡x+cos⁡x\frac{a\sin x + 2\cos x}{\sin x + \cos x}is increases for all values of x, then

A

a > 1

B

a < 1

C

a < 2

D

a > 2

Answer

a > 2

Explanation

Solution

f(x) = asin⁡x+2cos⁡xsin⁡x+cos⁡x\frac{a\sin x + 2\cos x}{\sin x + \cos x}

\ f(x) is ­ \ a × 1 – 2 × 1 > 0

Ž a > 2