If α+β=π2, β+γ=α and tan β=tan π4-γk, then the value of k is (A) 12 - Maths - Trigonometric Functions

Question

If α + β = π 2 ,   β + γ = α
  and   tan   β = tan   π 4 - γ
k , then the value of k is
(A) 1 2 (B) 2 (C) 1 3

Brijendra Pal · Accepted Answer

tan β=tanπ4-γkor β=π4-γk
1from given α=β+γand α+β=π2putting value of α,2β+γ=π22β=π2-γβ=π4-γ2
2compare equation 1 and 2 we can see that k =  2

If α + β = π 2 , β + γ = α and tan β = tan π 4 - γ k , then the value of k is (A) 1 2 (B) 2 (C) 1 3