Question

if A+B+C=180 prove that.. cos^2a(b+c/2)+cos^2a(a/2)=1

Answer 1

if a+b+c = 180
then whats
(b+c)/2 ?

Answer 2

in terms of a ?

Answer 3

can u find ?

Answer 4

What @hartnn wants you to realize is that: \[
\cos(90^\circ -x) = \sin(x)
\]

Answer 5

b+c/2=90-a/2

Answer 6

correct,
now whats
cos^2 (90 - a/2) = .... ?
use what wio said

Answer 7

cos^2(b+c/2)=sin^2a/2

Answer 8

now a/2 is an angle, like x

so whats sin^2 x + cos^2 x =....?

Answer 9

1

Answer 10

right,
so sin^2 (a/2) + cos^2 (a/2) will also be = 1 :)

Answer 11

thts it ?

Answer 12

thats what u wanted to prove,
that expression =1
we simplified it and got till sin^2(a/2) + cos^2(a/2)
which indeed =1

Answer 13

so yeah

Answer 14

thankss :)

Answer 15

welcome ^_^