Question

In right angle ABC ,prove that

cos (A+B/2)=sin(c/2)​

Answer 1

Answer:

Step-by-step explanation:

A+B+C=180

A+B=180-C

DIVIDE BOTH SIDE BY 2

A+B/2=180-C/2

A+B/2=90-C/2

COS(A+B/2)=cos(90-C/2)

COS(A+B/2)=SIN C/2. ( cos90-theta=sin theta) h.p.

Answer 2

$hello$

As the triangle is a rt. angle.So, let ang. C be the right ang.

=> A + B + C = 180°

=> A + B = 180° - C

=> (A + B)/2 = (180-C)/2 –––> [ dividing both side by 2]

=> (A+B)/2= 90° - C/2

=> Cos (A+B/2) = Cos ( 90° - C/2) –––> [multiplying both side by cos.]

=> Cos ( A+B/2) = Sin C/2

$hence \: proved$