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  • Which of the following is true for <img alt="\cos ^{2} \beta+\cos ^{2}(\alpha+\beta)-2 \cos \alpha \cos \beta \cos (\alpha+\beta)" src="http://entrancecorner.oncodecogs.com/gif.latex?%5Ccos%20

Which of the following is true for \cos ^{2} \beta+\cos ^{2}(\alpha+\beta)-2 \cos \alpha \cos \beta \cos (\alpha+\beta)

Option: 1

It is independent of \beta


Option: 2

It is independent of \alpha


Option: 3

It is independent of both \alpha\ and\ \beta


Option: 4

None of above


Answers (1)

best_answer

\\\cos ^{2} \beta+\cos ^{2}(\alpha+\beta)-2 \cos \alpha \cos \beta \cos (\alpha+\beta)\\=\cos ^{2} \beta+\cos (\alpha+\beta)[\cos (\alpha+\beta)-2 \cos \alpha \cos \beta] \\ =\cos ^{2} \beta+\cos (\alpha+\beta)[\cos \alpha \cos \beta-\sin \alpha \sin \beta-2 \cos \alpha \cos \beta]\\ =\cos ^{2} \beta-\cos (\alpha+\beta)[\cos \alpha \cos \beta+\sin \alpha \sin \beta] \\ =\cos ^{2} \beta-\cos (\alpha+\beta) \cos (\alpha-\beta) \\ =\cos ^{2} \beta-\left[\cos ^{2} \alpha-\sin ^{2} \beta\right]=\cos ^{2} \beta+\sin ^{2} \beta-\cos ^{2} \alpha \\ =1- \cos ^{2} \alpha

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Divya Prakash Singh

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