Question

If tan theta = 4, find sec theta

Show work plz

Answer 1

$\qquad$ $\purple{\bf{ {Answer = \: \:√17 }}}$

$\qquad$ $\twoheadrightarrow\bf tan\theta = 4 (Given)$

As we know –

$\qquad$ $\green{\twoheadrightarrow\bf sec^2\theta -tan^2\theta = 1 }$

Adding $\bf tan^2\theta$in both sides –

$\qquad$ $\twoheadrightarrow\sf sec^2\theta -tan^2\theta +tan^2\theta = 1 +tan^2\theta$

$\qquad$ $\twoheadrightarrow\sf sec^2\theta -\cancel{tan^2\theta} +\cancel{tan^2\theta} = 1 +tan^2\theta$

$\qquad$ $\twoheadrightarrow\sf sec^2\theta = 1 +tan^2\theta$

Substituting value of $\bf tan^2\theta$–

$\qquad$ $\twoheadrightarrow\sf sec^2\theta = 1+ 4^2$

$\qquad$ $\twoheadrightarrow\sf sec^2\theta = 1 + 16$

$\qquad$ $\twoheadrightarrow\sf sec^2\theta = 17$

$\qquad$ $\purple{\twoheadrightarrow\bf sec\theta = √17}$

• Henceforth, sec theta = √17.