Q. The value of `169e^{i(pi+sin^-1(12/13)+cos^-1(5/13))}` is:- A)   ` 119-120i` B)  `-i(120+119i)` C) `119+120i` D) none of these

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`e^i(pi+sin^(-1)(12/13)+cos^(-1)(5/13))`

`=cos(pi+sin^(-1)(12/13)+cos^(-1)(5/13))+isin(pi+sin^(-1)(12/13)+cos^(-1)(5/13))`

`=-cos(sin^(-1)(12/13)+cos^(-1)(5/13))-isin(sin^(-1)(12/13)+cos^(-1)(5/13))`

`sin^(-1)(12/13)=x`

`12/13=sin(x)`

`5/12=cos(x)`

`cos^(-1)(5/13)=x`

`Thus`

`e^i(pi+x+x)=-(cos(2x)+isin(2x))`

Correct choice D

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