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Question 14 : The value of cos^{2}\\frac{π}{8}) + cos^{2}\\frac{3π}{8}) + cos^{2}\\frac{5π}{8}) + cos^{2}\\frac{7π}{8}) is

- 1
- \\frac{3}{2})
- 2
- \\frac{9}{4})

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Now adding cos^{2}\\frac{π}{8}) and cos^{2}\\frac{7π}{8})

Then cos^{2}\\frac{3π}{8}) and cos^{2}\\frac{5π}{8})

cos^{2}\\frac{π}{8}) is same as cos^{2}\\frac{7π}{8})

cos^{2}\\frac{3π}{8}) is same as cos^{2}\\frac{5π}{8})

Question can be rephrased as 2cos^{2}\\frac{π}{8}) + 2cos^{2}\\frac{3π}{8})

\\frac{π}{8}) + \\frac{3π}{8}) = \\frac{π}{2})

cos(90 - θ) = sin θ

So, cos^{2}\\frac{3π}{8}) = sin^{2}\\frac{π}{8})

2cos^{2}\\frac{π}{8}) + 2sin^{2}\\frac{π}{8})

2[cos^{2} θ + sin^{2} θ]

2[1] = 2

The question is **" The value of cos ^{2}\\frac{π}{8}) + cos^{2}\\frac{3π}{8}) + cos^{2}\\frac{5π}{8}) + cos^{2}\\frac{7π}{8}) is " **

Choice C is the correct answer.

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