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Question
The expression `2 cos π/13. cos (9π)/13 + cos (3π)/13 + cos (5π)/13` is equal to ______.
Options
– 1
0
1
None of these
MCQ
Fill in the Blanks
Solution
The expression `2 cos π/13. cos (9π)/13 + cos (3π)/13 + cos (5π)/13` is equal to 0.
Explanation:
`2 cos π/13. cos (9π)/13 + cos (3π)/13 + cos (5π)/13`
= `2 cos π/13 . cos (9π)/13 + 2 cos (4π)/13 cos π/13`
= `2 cos π/13[cos (9π)/13 + cos (4π)/13]`
= `2 cos π/13[2 cos π/2. cos (5π)/26]` ...`[∵ cos π/2 = 0]`
= 0
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Trigonometric Functions of Triple Angle
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