Question

Sin(b+c/2) =cos A/2.if A, B and C are interior angle of a triangle ABC, then show that

Answer 1

Answer:

sin(b+c/2)=sin(90-A/2)

b+c/2=90-A/2 ( by taking LCM on RHS)

b+c/2=180-A/2 (cancel 2 on both the sides)

b+c=180-A

A+B+C=180

therefore A,B,C are the interior angles of triangle ABC

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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....:)