Find the maxima and minima of the following:
1.$f(x)= \cos x \left(\sin x+\sqrt{\sin^2x+\sin^2d} \right)$
2.$ f(x)=\frac{tan{(x+a)}}{tan{(x-a)}}$,
($a,d$ are constants)
Backround:This would be a straight forward problem if we use calculus.This problem is from S.L Loney, and we are not expected to use calculus. I actually don,t know how to start.It would be helpful if i could get a hint.
Here are somethings ,I think will work:
I know that $$-\sqrt{a^2+b^2}\le a\sin x+b\cos x\le \sqrt{a^2+b^2}$$.
Also I was run out of ideas of using inequalities like C-S,Am-Gm as the terms need not be positive.