1.

If cos4 θ – sin4 θ = 3/5, then the value of 1 – 2 sin2 θ is1). 02). 3/53). 1/34). 4/3

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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