supertorks
supertorks supertorks
  • 25-06-2020
  • Mathematics
contestada

prove that
1/(sec A - tan A) =sec A + tan A​

Respuesta :

Alfpfeu
Alfpfeu Alfpfeu
  • 25-06-2020

Answer:

Step-by-step explanation:

let s estimate the following

[tex](secA-tanA)(secA+tanA)=sec^2A-tan^2A=\dfrac{1}{cos^2A}-\dfrac{sin^2A}{cos^2A}=\dfrac{1-sin^2A}{cos^2A}=\dfrac{cos^2A}{cos^2A}=1[/tex]

as [tex]cos^2A+sin^2A=1[/tex]

it means that

[tex]\dfrac{1}{secA-tanA}=secA+tanA[/tex]

hope this helps

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