tan 2 arc cos x 1 0 lessthanorequalto arc cos x lessthanore

tan (2 arc cos x) = 1, 0 lessthanorequalto arc cos x lessthanorequalto pi sin (2 arc sec x) = squareroot 3/2, 0 lessthanorequalto arc sec x lessthanorequalto pi/2 4 sin^2 2x lessthanorequalto 1, [0, pi]

Solution

tan(2 arc cosx) =1

Taking tan^-1on both sides

2cos^-1x=tan^-11

2cos^-1x=pi/4,5pi/4

cos^-1x=pi/8,5pi/8

Taking cosine on both sides

x=cos pi/8    and    cos 5pi/8