Question

if a b and c are the interior angle of a triangle show that sin(B+C)/2=cos A/2​

Answer 1

Answer:

Step-by-step explanation:

a+b+c=180

b+c= 180-a

Therefore

Sin(180-a)/2 = cos ( a/2)

Sin(90-a/2) cos a/2

Cos (90-90+a/2)= cos a/2

Cos a/2 = cos a/2

Answer 2

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As we know, for any given triangle, the sum of all its interior angles is equals to 180°.

Thus,

A + B + C = 180° ….(1)

Now we can write the above equation as;

⇒ B + C = 180° – A

Dividing by 2 on both the sides;

⇒ (B + C)/2 = (180° – A)/2

⇒ (B + C)/2 = 90° – A/2

Now, put sin function on both sides.

⇒ sin (B + C)/2 = sin (90° – A/2)

Since,

sin (90° – A/2) = cos A/2

Therefore,

sin (B + C)/2 = cos A/2

Hope it's Helpful....:)