Question

IfA, B, C are interior angles of a triangle ABC, then show that
tan(a+b/2)=cot c/2

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Answer 1

Answer:

• sum of angels in a triangle is 180

Step-by-step explanation:

1. tan(a+b/2)=cot c/2 a+b+c=180 a+b=180-c both sides divided with 2 a+b/2=90-c/2 both sides multiply with tan tan(a+b/2)=tan(90 -c/2) tan(a+b/2)= cot(c/2) hence it is proven

Answer 2

To prove :

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

Solution :

A + B + C = 180° ( sum of angles of a ∆le = 180° )

A + B = 180° - C

divide both side by 2

A + B / 2 = 180° - C / 2

A + B / 2 = 180° / 2 - C / 2

A + B / 2 = 90° - C / 2

==> tan ( A + B / 2 ) = tan ( 90° - C / 2 )

tan ( A + B / 2 ) = cot ( C / 2 )

( bcoz ,, tan ( 90 - A) = cot A )

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