How do you evaluate $sec ({tan}^{- 1} (\sqrt{3}))$ $sec(tan^-1(sqrt3))$ without a calculator?

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How do you evaluate $sec ({tan}^{- 1} (\sqrt{3}))$ $sec(tan^-1(sqrt3))$ without a calculator?

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Answer 1 · 2016-10-12T21:56:34

$sec ({tan}^{- 1} (\sqrt{3})) = sec (60^{\circ}) = \frac{1}{cos (60^{\circ})} = \frac{1}{\frac{1}{2}} = 2$ $sec(tan^-1(sqrt3))=sec(60^@)=1/cos(60^@) = 1/(1/2)=2$

Explanation:

$sec ({tan}^{- 1} (\sqrt{3}))$ $sec(tan^-1(sqrt3))$ ->From the special triangle $30^{\circ} - 60^{\circ} - 90^{\circ}$ $30^@-60^@-90^@$ we have ${tan 60}^{\circ} = \sqrt{3}$ $tan 60^@=sqrt3$ hence $60^{\circ} = {tan}^{- 1} (\sqrt{3})$ $60^@=tan^-1(sqrt3)$

$sec (60^{\circ}) = \frac{1}{cos (60^{\circ})} = \frac{1}{\frac{1}{2}} = 2$ $sec(60^@)=1/cos(60^@) = 1/(1/2)=2$

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How do you evaluate $sec ({tan}^{- 1} (\sqrt{3}))$ $sec(tan^-1(sqrt3))$ without a calculator?

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How do you evaluate sec(tan−1(√3))sec(tan^-1(sqrt3)) without a calculator?

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How do you evaluate $sec ({tan}^{- 1} (\sqrt{3}))$ $sec(tan^-1(sqrt3))$ without a calculator?