Use trigonometric identities to solve cos2 theta sintheta e

Use trigonometric identities to solve cos^2 (theta) = sin(theta) exactly for 0 lessthanorequalto theta

Solution

cos^2 theta - sin^2 theta = sin theta

using identity on left side

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

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

1 - 2 sin^2 theta = sin theta

or

2 sin^2 theta + sin theta - 1 = 0

( sin theta + 1 ) ( 2 sin theta -1 ) = 0

sin theta = -1

theta = 3pi/2

sin theta = 1/2

theta = pi/6 , 5pi/6

solutions are

theta = pi/6 , 5pi/6 , 3pi/2