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Lelu [443]
3 years ago
9

Simplify this expressions

Mathematics
1 answer:
Nostrana [21]3 years ago
7 0

Answer:

\frac{36}{3 }  = 12

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sdas [7]

Step-by-step explanation:

Left hand side:

4 [sin⁶ θ + cos⁶ θ]

Rearrange:

4 [(sin² θ)³ + (cos² θ)³]

Factor the sum of cubes:

4 [(sin² θ + cos² θ) (sin⁴ θ − sin² θ cos² θ + cos⁴ θ)]

Pythagorean identity:

4 [sin⁴ θ − sin² θ cos² θ + cos⁴ θ]

Complete the square:

4 [sin⁴ θ + 2 sin² θ cos² θ + cos⁴ θ − 3 sin² θ cos² θ]

4 [(sin² θ + cos² θ)² − 3 sin² θ cos² θ]

Pythagorean identity:

4 [1 − 3 sin² θ cos² θ]

Rearrange:

4 − 12 sin² θ cos² θ

4 − 3 (2 sin θ cos θ)²

Double angle formula:

4 − 3 (sin (2θ))²

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Finally, apply Pythagorean identity and simplify:

4 − 3 (1 − cos² (2θ))

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