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OpenStudy (anonymous):

show that 1/cosx+1/sinx=Pi/2

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hartnn (hartnn):

@Floku Hi, \(\huge \color{red}{\text{Welcome to Open Study}}\ddot\smile\) 1/cosx+1/sinx cannot equal, pi/2 i am almost sure you meant \(\cos^{-1}x+\sin^{-1}x=\pi/2\) which is not same as what you wrote. \(\cos^{-1}x\)does not = 1/cos x its just inverse function of cos x

OpenStudy (anonymous):

That should be \[\sin^{-1} x and \cos^{-1} x\]... And \[\sin^{-1} x \] \[\neq 1/\sin x\]

hartnn (hartnn):

to prove that , you can use the identity, \(\sin (\pi/2 -y ) = \cos y \\(\pi/2 -y ) =\sin^{-1}[ \cos y] \\ \) now you can put, \(y=\cos^{-1}x\) and use \(\cos^{-1}[\cos \theta]=\theta \) to get your final result :)

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