Question

if sec - tan=4then prove that cos=8/17

Answer 1

Hi !

secθ - tanθ = 4                   -----> (1)

Multiplying and dividing by secθ +tanθ

 = secθ - tanθ × secθ +tanθ/secθ +tanθ

= sec²θ - tan²θ/secθ + tanθ = 4

we know that -->  sec²θ - tan²θ = 1

1/secθ + tanθ = 4

therefore ,

secθ + tanθ = 1/4                  ----> (2)

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Adding equations (1) and (2) :-

secθ - tanθ = 4

secθ + tanθ = 1/4   
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2secθ =  4 + 1/4
2secθ =   17/4

secθ =   17/4*2
         = 17/8

we know that 

cosθ =   1/secθ
         = 1/(17/8)
         = 8/17

Proved !