Question

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

Answer 1

@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

Answer 2

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

Answer 3

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 :)