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Question
The value of the expression sin6 θ + cos6 θ + 3 sin2 θ . cos2 θ is ______.
Options
0
2
3
1
MCQ
Fill in the Blanks
Solution
The value of the expression sin6 θ + cos6 θ + 3 sin2 θ . cos2 θ is 1.
Explanation:
sin6 θ + cos6 θ + 3 sin2 θ cos2 θ
= (sin2 θ)3 + (cos2 θ)3 + 3 sin2 θ cos2 θ
= (sin2 θ + cos2 θ) (sin4 θ + cos4 θ – sin2 θ cos2 θ) + 3 sin2 θ cos2 θ
= 1[(sin2 θ + cos2 θ)2 – 3 sin2 θ cos2 θ] + 3 sin2 θ cos2 θ
= 1 – 3 sin2 θ cos2 θ + 3 sin2 θ cos2 θ
= 1
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Trigonometric Functions of Allied Angels
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