Find the exact solutions of the equation cos 2a=square root(1-sin^2 a), 0

We have to determine the solutions for cos 2a = sqrt( 1 -
sin a)^2, lying in the range 0<a<180

cos 2a =
sqrt( 1 - (sin a)^2)

=> cos 2a = sqrt ( (cos
a)^2)

=> cos 2a = cos
a

=> 2*(cos a)^2 - 1 = cos
a

=> 2*(cos a)^2 - cos a - 1 =
0

=> 2*(cos a)^2 - 2cos a + cos a - 1 =
0

=> 2*cos a ( cos a + 1) + 1(cos a + 1) =
0

=> (2cos a + 1)( cos a + 1) =
0

2*cos a + 1 = 0

=>
cos a = -1/2

=> a = arc cos
(-1/2)

=> 120
degrees

cos a = 1

=> a
= arc cos (1)

=> a = 0, but it does not lie in the
interval.

The required value of a is 120
degrees.