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If tan theta = 4, find sec theta

Show work plz

If tan theta = 4, find sec theta Show work plz-example-1
User Dmarietta
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1 Answer

13 votes
13 votes


\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\thetain 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.

User Channa
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3.2k points