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

Question

Given that tan α = m/(m + 1), tan β = 1/(2m+ 1), then what is the value of α + β ? (A) 0 (B) (π/4) (C) (π/6) (D) (π/3)

Tardigrade Admin · Accepted Answer

As given, tan α = (m/m + 1) and tan β = (1/ 2m + 1) tan (α + β) = ( tan α + tan β/1 + tan α tan β) = ((m/m+1) + (1/2m+1)/1- (m)m+1 ×(1)2m+1 = (m(2m+1)+ (m+1)/(m+1)(2m+1) -m) = (2m2 + 2m +1/2m2 + 2m+1) = 1 So, α+β = (π/4)

Q. Given that $tan α = m / (m + 1), tan β = 1/ (2 m + 1),$ then what is the value of $α + β$ ?

0

$\frac{π}{4}$

$\frac{π}{6}$

$\frac{π}{3}$

Q. Given that tanα=m/(m+1),tanβ=1/(2m+1), then what is the value of α+β ?

0

4π​

6π​

3π​

As given, tanα=m+1m​ and tanβ=2m+11​ tan(α+β)=1+tanαtanβtanα+tanβ​ =1−m+1m​×2m+11​m+1m​+2m+11​​=(m+1)(2m+1)−mm(2m+1)+(m+1)​ =2m2+2m+12m2+2m+1​=1 So, α+β=4π​

Q. Given that $tan α = m / (m + 1), tan β = 1/ (2 m + 1),$ then what is the value of $α + β$ ?

$\frac{π}{4}$

$\frac{π}{6}$

$\frac{π}{3}$