Q. 344.1( 8 Votes )

Prove that: <span

Answer :

Formula: -


(i)


(ii) a2 – b2 = (a + b)(a – b)


L.H.S =


(sin4θ – cos4θ + 1) cosec2θ = ((sin2θ)2 – (cos2θ)2 + 1)cosec2θ


using formula (ii)


(sin4θ – cos4θ + 1) cosec2θ = ((sin2θ + cos2θ)(sin2θ – cos2θ) + 1)cosec2θ


(sin4θ – cos4θ + 1)cosec2θ = (sin2θ – cos2θ + 1)cosec2θ


(sin4θ – cos4θ + 1)cosec2θ = (sin2θ + (1 – cos2θ))cosec2θ


using formula(i)


(sin4θ – cos4θ + 1)cosec2θ = (sin2θ + sin2θ)cosec2θ


(sin4θ – cos4θ + 1)cosec2θ = 2sin2θ.cosec2θ



(sin4θ – cos4θ + 1)cosec2θ = 2


L.H.S = R.H.S


Hence, Proved.


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