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Summation of Determinant

prove y= [4si...

Question

prove y= [4sinx/(2+cosx)] - x is increasing on [0, /2]

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f (x) = \frac{4 sin x}{2 + cos x} - x

is an increasing function for

x ϵ (0, \frac{π}{2})

Q. Find the interval on which the following function are strictly increasing & strictly decreasing.

f (x) = \frac{4 s i n x - 2 x - x c o s x}{2 + c o s x}, 0 \leq x \leq 2 π

x + y = \frac{π}{2}

, then prove that

cos (x + y) = 0

Q. Find the intervals in which the function

f (x) = \frac{4 sin x - 2 x - x cos x}{2 + cos x}

is (i) increasing
(ii) decreasing

\frac{2 s i n 2 x - c o s x}{6 - {c o s}^{2} x - 4 s i n x}

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