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How to derive the equation from Line #1 to Line #2? I have tried different trigonometric functions but could not get it. enter image description here

1 Answers 1

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Use identities

$$\cos \frac{\theta_n }{2} =\cos \left(\theta_n -\frac{\theta_n }{2}\right)=\cos\theta_n \cos\frac{\theta_n }{2} +\sin\theta_n \sin\frac{\theta_n }{2}$$

and

$$\sin \frac{\theta_n }{2} =\sin \left(\theta_n -\frac{\theta_n }{2}\right)=\sin\theta_n \cos\frac{\theta_n }{2} -\cos\theta_n \sin\frac{\theta_n }{2}$$

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    Thanks @MotylaNogaTomkaMazura. I have tried to expand the equation but could not get what is shown in Line #2. Can you please show the steps? – 2017-01-05