Prove that cos cos^4 A - sin^4 A = cos²A×sin²A
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L.H.S = CosA + Cos2A = 1
= CosA = 1 - Cos2A
Therefore, Sin2A = CosA
R.H.S = Sin2A + Sin4A
= Sin2A + ( Sin2A )2
= CosA + Cos2A .........................( AS Sin2A = CosA )
= 1 ..........................( AS GIVEN )
Therefore Sin2A + Sin4A = CosA + Cos2A = 1
= CosA = 1 - Cos2A
Therefore, Sin2A = CosA
R.H.S = Sin2A + Sin4A
= Sin2A + ( Sin2A )2
= CosA + Cos2A .........................( AS Sin2A = CosA )
= 1 ..........................( AS GIVEN )
Therefore Sin2A + Sin4A = CosA + Cos2A = 1
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