Question

∝ + β = π / 2 and ∝ = β + Γ
then prove
1) tan ∝ = tan β + 2 tan Γ
2) tan∝.tanβ = 1

Answer 1

Answer:

  1) tan ∝ = tan β + 2 tan Γ

    2) tan∝.tanβ = 1

Step-by-step explanation:

2) ∝ + β = π / 2

β = π / 2 - ∝

tan β = tan ( π / 2 - ∝)

tan β = cot ∝

tan β = 1 / tan ∝

tan β . tan ∝ = 1

1) ∝ = β + Γ

∝ - β = Γ

tan (∝ - β) = tan Γ

tan ∝ - tan  β / 1 + tan∝.tan.β = tanΓ

tan ∝ - tan  β = tan Γ (1 + tan∝.tan.β)

tan ∝ - tan  β = tan Γ  (1 + 1)

tan ∝ - tan  β = 2tan Γ

tan ∝  = 2tan Γ + tan  β

Hence Proved

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