Question

Prove that cos²A/2 + cos²(B+C/2) =1​

Answer 1

Answer:

Cos²(A/2) + Cos²((B+C)/2) = 1

Step-by-step explanation:

Prove that cos²A/2 + cos²(B+C/2) =1​

Additional Detail Rquired is

A , B , C are Angles of a Triangle

or A + B + C = 180°

LHS

= Cos²(A/2) + Cos²((B+C)/2)

as A + B + C = 180°

=> B + C = 180° - A

Dividing by 2 both sides

=> (B + C)/2 = (180° - A)/2

=> (B + C)/2 =90° - A/2

= Cos²(A/2) + Cos²(90° - A/2)

As we know that

Cos(90 - x) = Sinx

= Cos²(A/2) + Sin²(A/2)

As we know that

Cos²x + Sin²x = 1

= 1

= RHS

= QED

Proved

Cos²(A/2) + Cos²((B+C)/2) = 1