Let f(x)=\frac{\sin(x-a)+\sin(x+a)}{\cos(x-a)-\cos(x+a)}, then

Correct Answer is : f is a constant function

f(x+2\pi)=f(x) but f(x+a)\neqf(x) for any 0

f is a strictly increasing function

f is a strictly decreasing function

KVPY SX SB Exam 2012 Question Paper

Question : 7 of 120

Marks: +1, -0

Let

f(x)={\sin(x-a)+\sin(x+a)}/{\cos(x-a)-\cos(x+a)}

, then

Solution:

f(x)={\sin(x-a)+\sin(x+a)}/{\cos(x-a)-\cos(x+a)}

={2\sin x. \cosa}/{2\sin x .\sin a} =\cot a

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