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#