5 pts Consider the following sinx1 cosx1 2 sinx cosx Prove

(5 pts) Consider the following: (sin(x1+ cos(x))-1 + 2 sin(x) cos(x) Prove the following identity by finding the appropriate equations for each eqn below. sin(x)+cos())sin (X)(eqn) sin(x) cos(x) cos (x) eqn = CO (x) + cos (a) +(eqn) sin(x) cos(x) eqn = = (eqn) + 2 sin(x) cos(x) eqn Note: You can earn partial credit on this problem

Solution

( sin x + cos x )^2 = 1 + 2 sin x cos x

( sinx + cos x)^2 = sin^2 x + 2 sin x cos x + cos^2 x

eqn = 2

= sin^2 x + cos^2 x + 2 sin x cos x

eqn = 2

= 1 + 2 sin x cos x

eqn = 1