Question

If a=b+c prove that tan a - tan b - tan c = tan a*tan b*tan c.

Answer 1

From the question , we can see that a - b - c = 0

using the identity

tan(a+b+c) =(tan(a) + tan(b) + tan(c) -tanatanbtanc )÷(1-(tanatanb+tanbtanc+ tanctana))

replace b with -b and c with -c

since a - b -c =0

lhs is zero

multiply the denominator on rhs on both sides , we then get , tan a - tan b - tan c - tan a*tan b*tan c=0

send tana*tan b*tan c to the other side ,

tan a - tan b - tan c = tan a*tan b*tan c.

Hence proved