Substitute x = 9tanθ into the expression \sqrt{81+ x^(2) } /x

Question

Substitute x = 9tanθ into the expression
`\sqrt{81+ x^(2) } /x`

Answer 1

`\frac{√(81+x^2)}x=(√(81+(9\tan\theta)^2))/(9\tan\theta)=(√(81+81\tan^2\theta))/(9\tan\theta)=(9√(1+\tan^2\theta))/(9\tan\theta)=(√(\sec^2\theta))/(\tan\theta)=(|\sec\theta|)/(\tan\theta)`