What is the extreme y=(cos(x))/(1+sin^2(x)) ?

The extreme y=(cos(x))/(1+sin^2(x)) is Maximum(2pin,1),Minimum(pi+2pin,-1)

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extreme y=(cos(x))/(1+sin^2(x))

extreme

Maximum (2 πn, 1), Minimum (π + 2 πn, - 1)

Solution steps

Find the critical points:

x = 2 πn, x = π + 2 πn

Domain of

\frac{cos ( x )}{1 + sin ^{2} ( x )} : - \infty < x < \infty

Find intervals:

Decreasing

: 2 πn < x < π + 2 πn,

Increasing

: π + 2 πn < x < 2 π + 2 πn

Plug the extreme point

x = 2 πn

into

\frac{cos ( x )}{1 + sin ^{2} ( x )} \Rightarrow y = 1

Maximum (2 πn, 1)

Plug the extreme point

x = π + 2 πn

into

\frac{cos ( x )}{1 + sin ^{2} ( x )} \Rightarrow y = - 1

Minimum (π + 2 πn, - 1)

Maximum (2 πn, 1), Minimum (π + 2 πn, - 1)

What is the extreme y=(cos(x))/(1+sin^2(x)) ?
The extreme y=(cos(x))/(1+sin^2(x)) is Maximum(2pin,1),Minimum(pi+2pin,-1)