Question

proved that√2.sin(π/4+theta)=costheta+sintheta

Answer 1

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Answer 2

Answer:

$\sqrt{2} \sin \left(\frac{\pi}{4}-\theta\right)=\cos \theta-\sin \theta$.Hence it is proved

Step-by-step explanation:

$\sin (A-B)=\sin A \cos B-\cos A \sin B$

$\sin \left(\frac{\pi}{4}-\theta\right)=\sin \frac{\pi}{4} \cos \theta-\cos \frac{\pi}{4} \sin \theta$

$\sin \left(\frac{\pi}{4}-\theta\right)=\frac{1}{\sqrt{2}} \cos \theta-\frac{1}{\sqrt{2}} \sin \theta$

$\sqrt{2} \sin \left(\frac{\pi}{4}-\theta\right)=\cos \theta-\sin \theta$

Hence proved