Question

If A,B,C are the angles of the triangle ABC. Show that
$cos^{2} ( \frac{A}{2} )+cos^{2} ( \frac{B+C}{2} )=1$

Answer 1

Hey there !!!!!!!!!

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

A,B,C are angles of triangle ABC

Sum of angles in a triangle = 180 degrees

A+B+C = 180

B+C = 180-A

=cos²(A/2) + cos²(B+C)/2 

=cos²(A/2) + cos²(180-A/2)

=cos²(A/2)+cos²(90-A/2)------Equation 1 

But cos(90-∅)= sin∅

So cos²(90-A/2) = sin²A/2

Equation 1 changes  to 

=cos²(A/2) + sin²(A/2)

But cos²∅+sin²∅=1

So ,

cos²(A/2) + sin²(A/2) = 1

LHS=RHS

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Hope this helped you...........