Find the value of sec−1(32)

Let sec−1(32)=x∴secx=32We know that cos6π=23∴secθ=cosθ1∴sec6π=32∴ comparing with secx=32x=6π∴sec−1(32)=6π

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Find the value of ^{-1} ( {2}{{3}} )

Question

Find the value of $sec^{- 1} (\frac{2}{3})$

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Theodore Discussed

Find the value of

sec^{- 1} (\frac{2}{3})

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Let

se c^{- 1} (\frac{2}{3}) = x

∴ sec x = \frac{2}{3}

We know that

cos \frac{π}{6} = \frac{3}{2}

∴ sec θ = \frac{1}{cos θ}

∴ sec \frac{π}{6} = \frac{2}{3}

∴

comparing with

sec x = \frac{2}{3}

x = \frac{π}{6}

∴ se c^{- 1} (\frac{2}{3}) = \frac{π}{6}

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