Question

6. If A, B and C are interior angles of a triangle ABC, then show that​

Answer 1

Answer:

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Answer 2

A +B+C=180                         (angle sum property of triangle)---------1

from 1  

B +C=180-A     ------------2

divide 2 on both sides of equation 2

we get

B+C the whole by 2=180-A the whole by 2

that is

B/2+C/2= 90-A/2

apply sin to both sides we get

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

sin 90-A/2 =cos A/2               ( complementary relation)        sub this in(a)

we get

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

hence proved

hope it helps you