How Do You Systematically Solve the Equation 2cos²x

Spruance · 2006-04-23T09:22:22+00:00

Dear all, How to solve this trigonometric equation systematically? 2cos^(2) x - cos x = 0, where x ∈ [0,360] Thanks in advance

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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How Do You Systematically Solve the Equation 2cos²x - cos x = 0?

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

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