Write $sin (x - \frac{3 π}{4})$ $sin(x-(3pi)/4)$ in terms of $sin x$ $sinx$ ?

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Answer 1 · 2017-04-11T14:56:58

$sin (x - \frac{3 π}{4}) = - \frac{1}{\sqrt{2}} (sin x + \sqrt{1 - {sin}^{2} x})$ $sin(x-(3pi)/4)=-1/sqrt2(sinx+sqrt(1-sin^2x))$

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

Hence $sin (x - \frac{3 π}{4}) = sin x cos (\frac{3 π}{4}) - cos x sin (\frac{3 π}{4})$ $sin(x-(3pi)/4)=sinxcos((3pi)/4)-cosxsin((3pi)/4)$

= $sin x cos (π - \frac{π}{4}) - cos x sin (π - \frac{π}{4})$ $sinxcos(pi-pi/4)-cosxsin(pi-pi/4)$

= $- sin x cos (\frac{π}{4}) - cos x sin (\frac{π}{4})$ $-sinxcos(pi/4)-cosxsin(pi/4)$

= $- sin x \times \frac{1}{\sqrt{2}} - cos x \times \frac{1}{\sqrt{2}}$ $-sinx xx1/sqrt2-cosx xx1/sqrt2$

= $- \frac{1}{\sqrt{2}} (sin x + cos x)$ $-1/sqrt2(sinx+cosx)$

= $- \frac{1}{\sqrt{2}} (sin x + \sqrt{1 - {sin}^{2} x})$ $-1/sqrt2(sinx+sqrt(1-sin^2x))$

Write sin(x-(3pi)/4)sin(x−3π4)sin(x-(3pi)/4) in terms of sinxsinxsinx?