# Trignometric functions and identities

## Homework Statement

How to quickly solve problems on maximum and minimum values of trig functions with help of calculus:
Ex. 10cos2x-6sinxcosx+2sin2x

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## The Attempt at a Solution

I know the method of simplification. But i want to do it quickly with calculus. How to do that??

Last edited:

HallsofIvy
Setting $f(x)= 10cos^2(x)- 6sin(x)cos(x)+ 2sin^2(x)$ then $f'(x)= -20cos(x)sin(x)- 6cos^2(x)+ 6sin^2(x)+ 4sin(x)cos(x)= -16sin(x)cos(x)- 6(sin^2(x)- cos^2(x))= 0$.