Question

Express `sin(x-(3pi)/4)` as a function of `sinx`?

Answer 1

`sin(x-(3pi)/4)=-1/sqrt2(sinx+sqrt(1-sin^2x))`

Explanation:

`sin(A-B)=sinAcosB-cosAsinB`

Hence `sin(x-(3pi)/4)`

= `sinxcos((3pi)/4)-cosxsin((3pi)/4)`

= `sinx*-1/sqrt2-cosx*1/sqrt2`

= `-1/sqrt2(sinx+cosx)`

= `-1/sqrt2(sinx+sqrt(1-sin^2x))`