Trigonometric function help please?

Question

Assume that 0 < thea< pi/2. Find an expression for the indicated trigonometric function.

Let x = 3 tanthea . Find sec thea.

Help please??

Answer 1

0 < θ < π/2

x = 3tanθ

Divide each side by 3

x / 3 = tanθ

Take square to each side

x² / 3² = tan²θ

But sec²θ = 1 + tan²θ

sec²θ = 1 + x² / 9

sec²θ = (9 + x² ) / 9

Take square root to each side

secθ = √(9 + x²) / √9

secθ = √(9 + x²) / 3.