(sin a - cos a)^2 + sin 2a
Expanding the square:
(sin^2 a - 2sin a * cos a + cos^2 a) + sin 2a
Since sin^2 a + cos^2 a = 1:
(1 - 2sin a * cos a) + sin 2a
Expanding sin 2a using the double angle identity:
(1 - 2sin a cos a) + 2sin a cos a
Simplifying the expression:
1
(sin a - cos a)^2 + sin 2a
Expanding the square:
(sin^2 a - 2sin a * cos a + cos^2 a) + sin 2a
Since sin^2 a + cos^2 a = 1:
(1 - 2sin a * cos a) + sin 2a
Expanding sin 2a using the double angle identity:
(1 - 2sin a cos a) + 2sin a cos a
Simplifying the expression:
1