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Question
The value of cos 6x is equal to ______.
Options
cos6 x – 48 cos3 x + 18 cos2 x – 1
3 cos2 x – 4 cos3 x + 18 cos2 x
32 cos6 x – 48 cos4 x + 18 cos2 x – 1
None of the above
MCQ
Fill in the Blanks
Solution
The value of cos 6x is equal to 32 cos6 x – 48 cos4 x + 18 cos2 x – 1.
Explanation:
cos 6x = cos 2(3x)
= 2 cos2 3x – 1 ...[∵ cos 2θ = 2 cos2 θ – 1]
= 2(cos 3x)2 – 1
= 2(4 cos3 x – 3 cos x)2 – 1 ...[∵ cos 3θ = 4 cos3 θ – 3 cos θ]
= 2(16 cos6 x + 9 cos2 x – 24 cos4 x) – 1
= 32 cos6 x – 48 cos4 x + 18 cos2 x – 1
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Trigonometric Functions of Triple Angle
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