Given that tan alpha = m / ( m + 1 ) , tan beta = 1 / ( 2m - Maths -

Question

Given that tan alpha = m / ( m + 1 ) , tan beta = 1 / ( 2m + 1 )
, then what is the value of alpha + beta ?

Varun.Rawat · Accepted Answer

We have,tan α = mm + 1    ;  tan β = 12m + 1tan α+β = tan α + tan β1 - tan α 
 tan β⇒tan α+β =mm+1 + 12m+11 - m m + 1 × 12m + 1⇒tan α+β = 2m2 + m + m + 1m+12m+12m2 +m + 2m + 1 - mm+12m+1⇒tan α+β =2m2 + 2m + 12m2 + 2m + 1⇒tan α+β =1⇒tan α+β = tan π4⇒α+β = π4

Given that tan alpha = m / ( m + 1 ) , tan beta = 1 / ( 2m + 1 ) , then what is the value of alpha + beta ?