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

### 1 Answer | Add Yours

`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**

### Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes