1.

Prove that: i) `sin^(-1)(3x-4x^(3))=3sin^(-1)x, |x| le 1/2` ii) `cos^(-1)(4x^(2)-3x)=3cos^(-1)x,1/2 le x le 1` iii) `tan^(-1)""(3x-x^(3))/(1-3x^(2))=3tan^(-1)x, |x| lt 1/sqrt(3)` iv) `tan^(-1)x+tan^(-1)""(2x)/(1-x^(2))=tan^(-1)""(3x-x^(3))/(1-3x^(2))`

Answer» i) Put `x=sintheta`, ii) Put `x=costheta`, iii) Put `x=tantheta`, iv) Use `tan^(-1)A+tan^(-1)B`


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