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  • The relationship between Arcsine and Arccosecant isOption: 1 <img alt="\mathrm{sin^{-1}x=cosec^{-1}\left (\frac{1}{x} \right ) }" src="http

The relationship between Arcsine and Arccosecant is

Option: 1

\mathrm{sin^{-1}x=cosec^{-1}\left (\frac{1}{x} \right ) }


Option: 2

\mathrm{sin^{-1}x=-cosec^{-1}\left (\frac{1}{x} \right )}


Option: 3

\mathrm{ sin^{-1}x=cosec^{-1}x }


Option: 4

\mathrm{sin^{-1}x=-cosec^{-1}x }


Answers (1)

best_answer

option (a) \mathrm{sin^{-1}x=cosec^{-1}\left (\frac{1}{x} \right ) }

Let,

\mathrm{ y=sin^{-1}x }

Then,

\mathrm{ sin\ y = x }

Since cosecant is the reciprocal of sine

\mathrm{ \frac{1}{sin\ y} = \frac{1}{x} }

\mathrm{ cosec\ y = \frac{1}{x} }

\mathrm{Y = cosec^{-1}\left ( \frac{1}{x} \right ) }

Therefore,

\mathrm{ sin^{-1}x= cosec^{-1}\left ( \frac{1}{x} \right ) }

Posted by

himanshu.meshram

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