How do you simplify the expression $sin (arctan (\frac{x}{5}))$ $sin(arctan(x/5))$ ?

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Answer 1 · 2016-06-20T16:15:00

$\pm \frac{x}{\sqrt{x^{2} + 25}}$ $+-x/sqrt(x^2+25)$ .

Let $a = a r c tan (\frac{x}{5})$ $a = arc tan (x/5)$ .

Then, $tan a = \frac{x}{5} \geq < 0$ $tan a = x/5 >=<0$ according as x>=<0#

Befittingly, the quadrant for a has to be chosen.

So, the given expression $= sin a = \pm \frac{x}{\sqrt{x^{2} + 25}}$ $= sin a = +-x/sqrt(x^2+25)$ .

How do you simplify the expression sin(arctan(x5))sin(arctan(x/5)) ?