How do I find the exact value of cos(2sin^-1(12/13))?

Reviewing for a trig exam and saw this. I don't remember learning anything like it. Thanks in advance!

1 Answer
Oct 17, 2017

-119/169.

Explanation:

Write, theta=sin^-1(12/13)," such that, "sintheta=12/13.....(1).

Hence, "the required value="cos(2sin^-1(12/13))=cos2theta,

=1-2sin^2theta,

=1-2(12/13)^2...........[because, (1)],

=1-288/169.

:. "the required value="-119/169.

I hope that helps!