Question

If tan[(C-A)/2] = K cot B/2 , find K​

Answer 1

Step-by-step explanation:

ANSWER

We have a[tanA−tan

2

1

(A+B)]

=b[tan

2

1

(A+B)−tanB] .....(1)

or a[

cosAcos

2

1

(A+B)

sinAcos

2

1

(A+B)−cosAsin

2

1

(A+B)

]

=b[

cos

2

1

(A+B)cosB

sin

2

1

(A+B)CosB−cos

2

1

(A+B)sinB

]

or

cosA

ksinAsin

2

1

(A−B)

=

cosB

ksinBsin

2

1

(A−B)

or sin

2

1

(A−B)(

cosA

sinA

−

cosB

sinA

)=0

or sin

2

1

(A−B)(tanA−tanB)=0.

From this equation, we conclude that A=B.