The value of 8 (sin6θ + cos6θ)

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The value of 8 (sin⁶θ + cos⁶θ) – 12 (sin⁴θ + cos⁴θ) is equal to

1. 20
2. – 20
3. – 4
4. 4

Correct Option: C

8 (sin⁶θ + cos⁶θ) – 12 (sin⁴θ + cos⁴θ)
= 8 {(sin²θ + cos²θ)³ – 3 sin²θ.cos²θ (sin²θ + cos²θ)} – 12 {(sin²θ + cos²θ)² – 2 sin²θcos²θ)}
= 8 (1 – 3 sin²θ . cos²θ) – 12 (1 – 2 sin²θ.cos²θ)
= 8 – 24 sin²θ.cos²θ – 12 + 24sin²θ.cos²θ = –4