In Δ A B C,(a-b)2 cos 2 (C/2)+(a +b)2 sin 2 (C/2) is equal to

Question

In Δ A B C,(a-b)2 cos 2 (C/2)+(a +b)2 sin 2 (C/2) is equal to (A) a2 (B) b2 (C) c2 (D) None of these

Tardigrade Admin · Accepted Answer

(a-b)2 cos 2 (C/2)+(a+b)2 sin 2 (C/2) =(a2+b2-2 a b) cos 2 (C/2) +(a2+b2+2 a b) sin 2 (C/2) =a2+b2+2 a b( sin 2 (C/2)- cos 2 (C/2)) =a2+b2-2 a b cos C =a2+b2-(a2+b2-c2) =c2

Q. In $Δ A BC, (a - b)^{2} cos^{2} \frac{C}{2} + (a + b)^{2} sin^{2} \frac{C}{2}$ is equal to

$a^{2}$

$b^{2}$

$c^{2}$

None of these

Q. In ΔABC,(a−b)2cos22C​+(a+b)2sin22C​ is equal to

a2

b2

c2

None of these

(a−b)2cos22C​+(a+b)2sin22C​ =(a2+b2−2ab)cos22C​ +(a2+b2+2ab)sin22C​ =a2+b2+2ab(sin22C​−cos22C​) =a2+b2−2abcosC =a2+b2−(a2+b2−c2) =c2

Q. In $Δ A BC, (a - b)^{2} cos^{2} \frac{C}{2} + (a + b)^{2} sin^{2} \frac{C}{2}$ is equal to

$a^{2}$

$b^{2}$

$c^{2}$