Question

If A,B and C are the interior angles of triangle ABC, show that sin (a+b/2) = cos c/2

Answer 1

as in Δabc
angle (a+b+c)=180
taking lhs from question
sin(a/2+b/2)
sin(180/2-c/2)
sin(90-c/2)
cos c/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....:)