Question

sin2a + cos2a = 3/2 , then the value of sin4a​

Answer 1

sin(4a) = 1.25

★sin²∅+cos²∅ = 1

★sin2∅ = 2sin∅.cos∅

∴sin4∅ = 2sin2∅.cos2∅

$sin2a + cos2a = \frac{3}{2} \\ ∴{(sin2a + cos2a)}^{2} = \frac{9}{4} \\ ∴ {sin}^{2} 2a + {cos}^{2} 2a + 2sin2a.cos2a = \frac{9}{4} \\ ∴1 + 2sin2a.cos2a = \frac{9}{4} \\ ∴sin2(2a) = \frac{9}{4} - 1 \\ ∴sin4a = \frac{9 - 4}{4} = \frac{5}{4}$

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