Equation Solving: sin(x) - cos(2x) = 0

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Homework Statement



0 = sin(x) - cos(2x)

Original problem asks to find the critical numbers of f(x) = 2cos(x) + sin(2x) . . . above is its derivative simplified and what I need to solve.
 
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reddawg said:

Homework Statement



0 = sin(x) - cos(2x)

Original problem asks to find the critical numbers of f(x) = 2cos(x) + sin(2x) . . . above is its derivative simplified and what I need to solve.

Have you ever seen cos2x in any formula?
 
Yes...

cos2x=1-2sin^2(x)

I can use that to my advantage I realizes...
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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