Question

6. IfA, B and C are interior angles of a triangle ABC, then show that
B+C
sin
COS
cia
2
2​

Answer 1

Answer:

hey mate

here is ur answer

A+B+C=180 (angle sum property)

B+C=180-A

B+C/2=90-A/2

Sin(B+C/2)=Sin(90-A/2)

Sin(B+C/2)=CosA/2

hope it helps u

thanks for giving me a chance to help you

гค๔ђєץ гค๔ђєץ

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....:)