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Question
The value of `cos π/8 + cos (3π)/8 + cos (5π)/8 + cos (7π)/8` is ______.
Options
0
– 2
4
`1/sqrt(3)`
MCQ
Fill in the Blanks
Solution
The value of `cos π/8 + cos (3π)/8 + cos (5π)/8 + cos (7π)/8` is 0.
Explanation:
We have, `cos π/8 + cos (3π)/8 + cos (5π)/8 + cos (7π)/8`
= `cos π/8 + cos (3π)/8 + cos(π - (3π)/8) + cos(π - π/8)`
= `cos π/8 + cos (3π)/8 - cos (3π)/8 - cos π/8` ...[∵ cos(π – θ) = – cos θ]
= 0
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Trigonometric Functions of Allied Angels
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