Inverse Trig Equation Comparison: Arcsec vs Arctan

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Homework Statement



I have knocked a problem down to:

-arcsec \frac{3x}{4}

but my textbook gives the answer as:

arctan \frac{4}{\sqrt{9x^2 - 16}}

Are these somehow equivalent?

Thanks

Homework Equations





The Attempt at a Solution

 
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I don't think so. However, I get arccsc (3x/4) being equal to arctan(4/sqrt(9x^2 - 16))
 

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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