Question

If sec theta =x+1/x then prove that sec theta +tan theta =2x or 1/2x

Answer 1

The given question is incorrect.

Correct question:

If sec theta =x+1/4x then prove that sec theta +tan theta =2x or 1/2x.

Solution;

• Given that Secθ = x+1/4x

we  know that  1+tan²θ = sec²θ

or tan²θ = (1+1/4x)²

on expanding we get

tan²θ = ( x²+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-1/4x²)

or tan²θ = (1-1/4x) or - (1-1/4x²)

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