If sin² θ - cos² θ = 1/2 , what is the value of sin⁴θ – cos⁴ θ ?
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Answer:
From the above equation, we get
cosθ=sinθ
Hence
θ=45
Therefore
sin⁴θ+cos⁴θ
=sin⁴45+cos⁴45
=2×(1/root2)⁴
=2×1/4
=1/2
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