Solution :
R.H.S. = tan(60∘ + A)tan(60∘ – A)
= (tan60∘+tanA1−tan60∘tanA)(tan60∘−tanA1+tan60∘tanA)
= (√3+tanA1−√3tanA)(√3−tanA1+√3tanA)
= 3−tan2A1−3tan2A = 3cos2A−sin2Acos2A−3sin2A
= 2cos2A+cos2A−2sin2A+sin2A2cos2A−2sin2A−sin2A−cos2A
= 2(cos2A−sin2A)+cos2A+sin2A2(cos2A−sin2A)−(sin2A+cos2A)
= 2cos2A+12cos2A−1 = L.H.S
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