QQuestion
If cos⁴θ – sin⁴θ = \frac{2}{3} , find the value of 1 – 2 sin²θ.
✓Answer
cos⁴θ – sin⁴θ = (cos²θ – sin²θ)(cos²θ + sin²θ).
or, \frac{2}{3} = (cos²θ – sin²θ) × 1
or, \frac{2}{3} = (1 – sin²θ – sin²θ)
or, 1 – 2sin²θ = \frac{2}{3}
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