The solution set of the equation `sin^(-1)x=2 tan^(-1)x` isA. `{1,2}`B. `{-1,2}`C. `{-1,1}`D. `{1,1//2,0}`

The solution set of the equation `sin^(-1)x=2 tan^(-1)x` isA. `{1,2}`B

1.	The solution set of the equation `sin^(-1)x=2 tan^(-1)x` isA. `{1,2}`B. `{-1,2}`C. `{-1,1}`D. `{1,1//2,0}`
Answer» Clearly LHS of the given equation is meaningful for `x in [-1,1]` and RHS is defined for all x`x in R` So the given equation exists for `x in [-1,1]` Now `sin^(-1)x=2 tan^(-1)` `rarr sin^(-1) x= sin^(-1)((2x)/(1+x^(2)))` `rarr x^(3)=x rarr x=0,1,-1`

`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)=`
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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)`