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The value of the following is : 3(sin4θ + cos4θ) + 2(sin6θ + cos6θ) + 12sin2θ cos2θ
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- 0
- 3
- 2
- 5
Correct Option: D
Expression = 3(sin4 θ + cos4 θ) + 2(sin6 θ + cos6 θ) + 12 sin² θ. cos² θ
= 3{(sin² θ + cos² θ)² – 2 sin² θ . cos² θ} + 2{(sin² θ + cos² θ)3 – 3 sin² θ . cos² θ (sin² θ + cos² θ) + 12 sin² θ . cos² θ [∵ a² + b²
= (a + b)² – 2ab ; a3 + b3
= (a + b)3 – 3ab (a + b)]
= 3 (1 – 2 sin²θ. cos²θ) + 2 (1 – 3 sin²θ . cos²θ) + 12 sin²θ. cos²θ = 3 – 6 sin²θ . cos²θ + 2 – 6
sin²θ cos²θ + 12 sin²θ . cos²θ=5
