The value of cot[cos−1(257)] is

we have cot[cos−1(257)]Let cos−1257=x⇒cosx=257∴sinx=1−cos2x=1−(257)2=625625−49=2524∴cotx=sinxcosx=2524257=247⇒x=cot−1(247)=cot−1 (257)∴cot(cos−1257)=cot (cos−1247)=247 [∵cos−1247=cos−1257]

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The value of [cos^{-1}({7}{25})] is

Question

The value of $cot [co s^{- 1} (\frac{7}{25})]$ is

\frac{25}{24}

\frac{25}{7}

\frac{24}{25}

\frac{7}{24}

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Text solutionVerified

we have

cot [co s^{- 1} (\frac{7}{25})]

Let

cos^{- 1} \frac{7}{25} = x

\Rightarrow cos x = \frac{7}{25}

∴ sin x = 1 - cos^{2} x = 1 - (\frac{7}{25})^{2}

= \frac{625 - 49}{625} = \frac{24}{25}

∴ cot x = \frac{cos x}{sin x} = \frac{\frac{7}{25}}{\frac{24}{25}} = \frac{7}{24}

\Rightarrow x = cot^{- 1} (\frac{7}{24}) = cot^{- 1} (\frac{7}{25})

∴ cot (cos^{- 1} \frac{7}{25}) = cot (cos^{- 1} \frac{7}{24}) = \frac{7}{24} [∵ cos^{- 1} \frac{7}{24} = cos^{- 1} \frac{7}{25}]

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Question Text	The value of $cot [co s^{- 1} (\frac{7}{25})]$ is
Answer Type	Text solution:1
Upvotes	150

The value of cot[cos−1(257​)] is

Text solutionVerified

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The value of $cot [co s^{- 1} (\frac{7}{25})]$ is