Question

for triangle ABC show that tan b + c by 2 is equal to COT a by 2​

Answer 1

Solution==>

In triangle, Sum is 180°

therefore,

A+B+C=180

B+C=180°-A.......(1)

tan(b+c)/2=cot a/2

L.H.S==>

tan(b+c)/2.....(2)

put (1) in (2)

tan(180°-A)/2

tan(180°/2 -A/2)

tan(90°-A/2)

cot A/2

Hence, proved!

<=> identities used

1)tanA=cot(90°-A)

Answer 2

Answer:

tan(b+c)/2=cot a/2

Step-by-step explanation:

A+B+C=180

B+C=180°-A ->(1)

tan(b+c)/2=cot a/2

L.H.S ->

tan(b+c)/2 ->(2)

Substitute (1) in (2)

tan(180°-A)/2

tan(180°/2 -A/2)

tan(90°-A/2)

cot A/2

L.H.S = R.H.S

Hence Verified