Question

(b-c)^2 cos^2 (A/2) + (b+c)^2 sin^2 (A/2) =
1) a 2) a^2 3) 2a² 4) a²/2​

Answer 1

Answer:

answer is

Step-by-step explanation:

a^2 is the correct

100%correct

Answer 2

Answer:

$\bold\red{(2){a}^{2}}$

Step-by-step explanation:

Let's denote angle A as Alpha.

Now,

Given,

${(b - c)}^{2} { \cos}^{2} \frac{ \alpha }{2} + {(b + c)}^{2} { \sin}^{2} \frac{ \alpha }{2}$

Expanding,

we get,

$= ( {b}^{2} + {c}^{2} - 2bc) { \cos }^{2} \frac{ \alpha }{2} + ( {b}^{2} + {c}^{2} + 2bc) { \sin }^{2} \frac{ \alpha }{2} \\ \\ = {b}^{2}( { \sin}^{2} \frac{ \alpha }{2} + { \cos }^{2} \frac{ \alpha }{2} ) + {c}^{2} ( { \sin }^{2} \frac{ \alpha }{2} + { \cos}^{2} \frac{ \alpha }{2} ) + 2bc( { \sin }^{2} \frac{ \alpha }{2} - { \cos }^{2} \frac{ \alpha }{2} )$

But,

we know that,

${ \sin}^{2} x + { \cos }^{2} x = 1 \\ \\ and \\ \\ { \cos }^{2} x - { \sin}^{2} x = \cos(2x)$

Therefore,

we get,

$= {b}^{2} + {c}^{2} - 2bc \cos( \alpha )$

$= { \alpha }^{2}$

Hence,

the correct option is $\bold{(2){a}^{2}}$