(sin a + cos a)^2 - 2sin a*cos a
Expanding the left side using the formula (a+b)^2 = a^2 + 2ab + b^2:
= sin^2 a + 2sin a cos a + cos^2 a - 2sin a cos a
Now simplify:
= sin^2 a + cos^2 a
Since sin^2 a + cos^2 a = 1 (from the Pythagorean trigonometric identity), the final result is:
= 1
(sin a + cos a)^2 - 2sin a*cos a
Expanding the left side using the formula (a+b)^2 = a^2 + 2ab + b^2:
= sin^2 a + 2sin a cos a + cos^2 a - 2sin a cos a
Now simplify:
= sin^2 a + cos^2 a
Since sin^2 a + cos^2 a = 1 (from the Pythagorean trigonometric identity), the final result is:
= 1