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Question
The value of `(1 + cos π/6)(1 + cos π/3)(1 + cos (2π)/3)(1 + cos (7π)/6)` is equal to ______.
Options
`3/16`
`3/8`
`3/4`
`1/2`
MCQ
Fill in the Blanks
Solution
The value of `(1 + cos π/6)(1 + cos π/3)(1 + cos (2π)/3)(1 + cos (7π)/6)` is equal to `underlinebb(3/16)`.
Explanation:
`(1 + cos π/6)(1 + cos π/3)(1 + cos (2π)/3)(1 + cos (7π)/6)`
= `(1 + sqrt(3)/2)(1 + 1/2)(1 - 1/2)(1 - sqrt(3)/2)`
= `(1 - 3/4)(1 - 1/4)`
= `1/4 xx 3/4`
= `3/16`
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Trigonometric Functions of Triple Angle
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