Q. 335.0( 1 Vote )

Sin8θ

Answer :

formula: - (i) sin2θ + cos2θ = 1


(ii) a2 – b2 = (a + b)(a – b)


taking L.H.S


Sin8θ – cos8θ = (sin4θ)2 – (cos4θ)2


Sin8θ – cos8θ = (sin4θ + cos4θ)(sin4θ – cos4θ)


using formula (i)


Sin8θ – cos8θ = ((sin2θ)2 + (cos2θ)2)((sin2θ)2 – (cos2θ)2)


using formula (ii)


Sin8θ – cos8θ = ((sin2θ + cos2θ)2 – 2sin2θcos2θ)) (sin2θ + cos2θ)(sin2θ – cos2θ)


Sin8θ – cos8θ = (1 – 2sin2θcos2θ)(sin2θ – cos2θ)


Sin8θ – cos8θ = (sin2θ – cos2θ)(1 – 2sin2θcos2θ)


L.H.S = R.H.S


Hence, Proved.


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