Question

if a+b=pie/2 and b+y=a.then find the value of tan a. ​

Answer 1

Answer:

(3) tan β + 2 tan γ

Solution:

Given,

α + β = π/2 and β + γ = α

Thus, γ = α – β

Taking “tan” on both sides,

tan γ = tan(α – β)

= (tan α – tan β)/ (1 + tan α tan β)

= (tan α – tan β)/ [1 + tan α tan(π/2 – α)]

= (tan α – tan β)/ [1 + tan α cot α]

tan γ = (tan α – tan β)/ (1 + 1)

2 tan γ = tan α – tan β

Therefore, tan α = tan β + 2 tan γ