Can e^i(x+y) + e^-i(x+y) be Simplified to 2cosxcosy?

ramses07 · 2011-04-21T03:15:03+00:00

Homework Statement im wondering if e^i(x+y) + e^-i(x+y) can be simplified to 2cosxcosy Homework Equations 2cosx= e^ix + e^-ix so i separated e^i(x+y) + e^-i(x+y) into; e^ix(e^iy) + e^-ix(e^-iy) can that become 2cosxcosy?

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

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