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1)Prove :The value of log 2 [ cos 2 ( α + ß ) + cos 2 ( α - ß ) - cos2α.cosß] ++independent of both ß and a.

1)Prove :The value of log 2 [ cos2(α+ß) + cos2(α - ß) - cos2α.cosß]
++independent of both ß and a.



Grade:11

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
9 years ago
Ans:Hello student, please find answer to your question
L = log_{2}[cos^{2}(\alpha +\beta )+cos^{2}(\alpha -\beta )-cos2\alpha .cos\beta ]
L = log_{2}[(cos\alpha.cos\beta-sin\alpha .sin\beta)^{2}+(cos\alpha.cos\beta+sin\alpha .sin\beta)^{2}-cos2\alpha .cos\beta ]L = log_{2}[2cos^{2}\alpha.cos^{2}\beta+2sin^{2}\alpha .sin^{2}\beta-cos2\alpha .cos\beta ]
L = log_{2}[2cos^{2}\alpha.cos^{2}\beta+2(1-cos^{2}\alpha).(1-cos^{2}\beta)-cos2\alpha .cos\beta ]
L = log_{2}[4cos^{2}\alpha.cos^{2}\beta+2-2cos^{2}\alpha-2cos^{2}\beta-cos2\alpha .cos\beta ]
L = log_{2}[cos2\alpha .cos2\beta -cos2\alpha .cos\beta ]
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