Respuesta :

LHS = tan(45° - A)

[tex]=\frac{tan45-tanA}{1+tan45tanA}[/tex]

[tex]=\frac{1-tanA}{1+tanA} =RHS[/tex]

Answer:

See below ~

Step-by-step explanation:

Solving :

Taking the LHS :

  • tan (45 + A)

Formula :

  • tan (x + y) = tan x + tan y / 1 - (tan x)(tan y)

Solving :

  • tan (45 + A) = tan 45° + tan A / 1 - (tan 45°)(tan A)
  • tan (45 + A) = 1 + tan A / 1 - tan A (because tan 45° = 1)
  • Equal to the RHS

∴ Hence, it is proved √