Math, asked by Ritikagupta12, 1 year ago

if sec theta = x + 1/4x, prove thatvsec theta + tan theta = 2x or 1/2x.​

Answers

Answered by ayushghogre7
235

Step-by-step explanation:]

Sec A = x + 1/4x

As,           1 + Tan²A = Sec²A

Tan²A = (x+ 1/4x)² - 1

          = x² +2x*1/4x + 1 /16x² -1

          = x² + 1/16² - 1/2

          = (x-1/4x)²

 Tan²A = x-1/4x     or     Tan²A = -(x-1/4x)

Substitute the value of SecA and TanA in the given equation Sec A +Tan A

L.H.S = SecA + TanA

         = x + 1/4x - x + 1/4x

         = 2/4x

         =R.H.S

Hope it helps

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Answered by TheBandits
43

Given that secθ = x+1/4x

1+tan²θ = sec²θ

or tan²θ = sec²θ – 1

on expanding

tan²θ = ( x+1/4x)² -1

or tan²θ = ( x²+1/16x² + 1/2 -1 )

or tan²θ = (x² +1/16x² -1/2 )

or tan²θ =  x² +1/16x²-1/2

or tan²θ = (x-1/4x)^2

or tan²θ = +(x-1/4x) or – (x-1/4x)

when tanθ = (x-1/4x) we get

secθ+tanθ = x+1/4x + x-1/4x = 2x

when tanθ = -(x-1/4x)

secθ+tanθ = (x+1/4x) – (x-1/4x) = 1/2x

Hence  

secθ+tanθ = (x+1/4x) – (x-1/4x) = 1/2x

and secθ+tanθ = x+1/4x + x-1/4x = 2x

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