Question

sin theta - cos theeta =root 2 sin theta prove that sin theta + cos theta = root 2 cos theta

Answer 1

Answer:

Qed

Step-by-step explanation:

Let say thetha = a

Sina - Cosa = root2 sina

Squraing both sides

Sin^2a + Cos^2a - 2SinaCosa = 2 Sin^2a

1 - 2SinaCosa = 2Sin^2a

2SinaCosa = 1 - 2Sin^2a

(Sina + cosa)^2 = sin^2a + cos^2a + 2sinacosa

(Sina + cosa)^2 = 1 + 1 -2Sin^2a

(Sina+Cosa)^2 = 2 - 2Sin^2a

(Sina + Cosa)^2 = 2 (1-Sin^2a)

(Sina + Cosa)^2 = 2 Cos^2a

Sina + Cosa = root 2 Cosa

Qed