How do you find the value of cos [2 Sin^-1 (-24/25)]?

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Answer 1 · 2015-05-17T21:31:52

For any angle $theta$ , we have $cos 2theta = cos^2 theta - sin^2 theta$ . We also know that $sin^2 theta + cos ^2 theta = 1$ .

So $cos 2theta = cos^theta - sin^2theta$

$= (1-sin^2 theta)-sin^2theta$

$=1-sin^2theta$

If $theta = sin^-1(-24/25)$

then $sin theta = -24/25$

and $cos 2theta = 1-sin^2theta$

$=1-(-24/25)^2$

$=1-(24/25)^2$

$=1-24^2/25^2$

$=(25^2-24^2)/25^2$

$=((24+1)^2-24)/25^2$

$=((2xx24)+1)/25^2$

$=49/625$