Question

Cot A+B by 2 tan A-B by 2​

Answer 1

Answer:

cot(a+b/2).tan(a-b/2)

=tan(a-b/2)/tan(a+b/2)

=((tan a-tanb/2)/1+tana.tanb/2)*((1-tana.tanb/2)/(tana+tanb/2))

=(tana-tan^2(a).tanb/2-tanb/2+tana.tan^2(b/2))/(tana+tanb/2+tan^2(a).tanb/2+tana.tan^2(b/2))

let a=tan a and b=tan b

=a-b+a^2.b-a.b^2/a+b+a^2.b+ab^2

=(a(1+ab)-b(1+ab))/(a(1+ab)+b.(1+ab))

=(a+b)(1+ab)/(a-b)(1+ab)

=a+b/a-b

=tan a+tan b/tan a-tan b

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