Efficient Simplification of cos(sin^{-1}(9x))

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I need to simplify this expression. How do I go upon that? cos(sin^{-1}(9x))
 
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astr0 said:
I need to simplify this expression. How do I go upon that? cos(sin^{-1}(9x))
What have you tried? Before we can help you, you need to have made an effort at solving the problem for yourself.
 
Mark44 said:
What have you tried? Before we can help you, you need to have made an effort at solving the problem for yourself.
I agree with Mark!
 
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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