Question

If tanA=x/(x+1) and tanB=1/(2x+1), then A+B is equal to

Answer 1

Apply,

tan (A+B) = [tan (A) + tan (B)]/(1-tan (A)*tan (B))

putting given values,

tan (A+B)= (x/x+1 +1/2x+1)/(1-x/(x+1)(2x+1))

or,

tan (A+B) = (x(2x+1)+x+1)/[(x+1)*(2x+1)-x]

Value of both numerator and denominator on R.H.S. are equal hence,

tan (A+B) = 1

or

A+B = 45.