Q. 49

If tanA + sinA =

Answer :

Given: -


(i) m = tanA + sinA


(ii) n = tanA – sinA


Proof:


Taking L.H.S


(m2 – n2)2 = (tanA + sinA)2 – (tanA – sinA)2


(m2 – n2)2 = (tan2A + sin2A + 2tanAsinA – (tan2A + sin2A – 2tanAsinA))2


(m2 – n2)2 = (4tanAsinA)2


(m2 – n2)2 = 16tan2Asin2A


(m2 – n2)2 = 16tan2A(1 – cos2A)


(m2 – n2)2 = 16(tan2A – tan2Acos2A)



(m2 – n2)2 = 16(tan2A + sin2A) (tan2A – sin2A)


(m2 – n2)2 = 16 mn


Hence, Proved.


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