Question

${sin}^{4} theta - {cos}^{4}theta =$
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Answer 1

Answer:

We know that,

sin2θ + cos2θ = 1

2 sinθ cosθ = sin2θ

(a + b)2 = a2 + b2 + 2ab

Given, X = sin4θ + cos4θ

⇒ X = (sin2θ + cos2θ)2 – 2sin2θcos2θ

⇒ X = 1 – (sin22θ)/2

We know that, 0 ≤ sin2θ ≤ 1

 ∴ ½ ≤ X ≤ 1

Thank you :)