solve `sin^(-1) x le cos^(-1) x`

1.	solve `sin^(-1) x le cos^(-1) x`
Answer» `cos^(-1) x ge sin^(-1) x` or `(pi)/(2) - sin^(-1) x ge sin^(-1) x` `(pi)/(2) ge 2 sin^(-1) x` `(-pi)/(2) le sin^(-1) x le (pi)/(4)` or `-1 le x le sin ((pi)/(4))` `rArr x in [-1, (1)/(sqrt2)]`

Discussion

`tan^(-1)[(cosx)/(1+sinx)]`is equal to`pi/4-x/2,forx in (-pi/2,(3pi)/2)``pi/4-x/2,forx in (-pi/2,pi/2)``pi/4-x/2,forx in (-pi/2,pi/2)``pi/4-x/2,forx in (-(3pi)/2,pi/2)`
The value of `sin^(-1)(sin12)+sin^(-1)(cos12)=`
Find the principal value of `sin^(-1)(-1/sqrt2)-2tan^(-1)(-sqrt3)+cos^(-1)(-1/2)`.
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If `x , y , z in [-1,1]`such that `sin^(-1)x+sin^(-1)y+sin^(-1)z=-(3pi)/2,`find the value of `x^2+y^2+z^2dot`A. 1B. 3C. `(3pi^(23))/(4)`D. `3pi^(2)`
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Find the principal value of `sin^(-1)(-1/sqrt2)+tan^(-1)(-1/sqrt3)+sec^(-1)(2)`