1.

Prove that cos4θ – sin4θ = 2cos2θ – 1

Answer»

L.H.S. cos4θ – sin4θ 

= (cos2θ)2 – (sin2θ)2 

= (cos2θ + sin2θ) (cos2θ – sin2θ) 

= 1 . (cos2θ – (1 – cos2θ) = cos2θ – 1 + cos2θ 

= 2cos2θ – 1 = R.H.S.



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