Question

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Answer 1

Step-by-step explanation:

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 tanθ = +(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