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

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Answer 1 · 2018-01-31T15:11:22

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

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

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

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

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

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

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

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