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If cos4 θ – sin4 θ = 3/5, then the value of 1 – 2 sin2 θ is1). 02). 3/53). 1/34). 4/3 |
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Answer» cos4 θ – sin4 θ = (cos2 θ)2 – (sin2 θ)2 We know that, a2 – b2 = (a + b) (a – b) Hence, (cos2 θ)2 – (sin2 θ)2 = (cos2 θ + sin2 θ) (cos2 θ - sin2 θ) But, (cos2 θ + sin2 θ) = 1 Hence, (cos2 θ)2 – (sin2 θ)2 = (cos2 θ - sin2 θ) ALSO cos 2θ = cos2 θ - sin2 θ = 1 – 2sin2 θ Therefore, cos4 θ – sin4 θ = 1 – 2sin2 θ = 3/5 |
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