Prove that cos^2(15) + cos^2(45) + cos^2(75) = 3/2

Question

Prove that cos^2(15) + cos^2(45) + cos^2(75) = 3/2

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Kaylee 1 month 2021-08-18T10:01:22+00:00 1 Answer 0 views 0

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    2021-08-18T10:03:06+00:00

    Answer:

    cos^2(15) + cos^2 (45) + cos ^2(75) = 3/2. (given) Now cos^2(15) + cos^2(45) + cos^2(90-15) . cos^2 15 + cos^2 45+ sin^2 15. cos^2 15+ sin^2 15 + cos^2 45. [cos^2 15+ sin^2 15]= 1. ( according to trigonometric identity). i.e 1+ cos^2 45° = 1+ (1/√2)^2 = 1+ 1/2 = 3/2. Hence it is proved. Hope this helps you.

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