tan a = m/(m+1) ; tan b = 1/(2m+1) Find a+b

Question

No details are given as to if the trignometric ratios are from the same triangle.

The options are

π/2

π/3

π/4

π/6

I wish someone would tell me how to solve this question and why there isa pi in a trigonometry question

Answer 1

It doesn’t matter if a and b are from the same triangle or not, you can use trig identities to solve it

tan a = m/(m+1)

tan b = 1/(2m+1)

tan (a+b) = (Tan a + Tan b) / (1 - Tan a * Tan b)

tan (a+b) = ( m/(m+1) + 1/(2m+1) )/

(1-m/(m+1)*1/(2m+1)

evauluating the above will give

tan(a+b) = 1 which means a+b is pi/4