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Question 14 : The value of cos²\\frac{π}{8}) + cos²\\frac{3π}{8}) + cos²\\frac{5π}{8}) + cos²\\frac{7π}{8}) is

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

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Video Explanation

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Explanatory Answer

Now adding cos²\\frac{π}{8}) and cos²\\frac{7π}{8})

Then cos²\\frac{3π}{8}) and cos²\\frac{5π}{8})

cos²\\frac{π}{8}) is same as cos²\\frac{7π}{8})

cos²\\frac{3π}{8}) is same as cos²\\frac{5π}{8})

Question can be rephrased as 2cos²\\frac{π}{8}) + 2cos²\\frac{3π}{8})

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

cos(90 - θ) = sin θ

So, cos²\\frac{3π}{8}) = sin²\\frac{π}{8})

2cos²\\frac{π}{8}) + 2sin²\\frac{π}{8})

2[cos² θ + sin² θ]

2[1] = 2

The question is " The value of cos²\\frac{π}{8}) + cos²\\frac{3π}{8}) + cos²\\frac{5π}{8}) + cos²\\frac{7π}{8}) is "

Hence, the answer is 2

Choice C is the correct answer.

 

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