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Prove that 2cos2A+12cos2A1 = tan(60 + A)tan(60 – A)

Solution :

R.H.S. = tan(60 + A)tan(60 – A)

= (tan60+tanA1tan60tanA)(tan60tanA1+tan60tanA)

= (3+tanA13tanA)(3tanA1+3tanA)

= 3tan2A13tan2A = 3cos2Asin2Acos2A3sin2A

= 2cos2A+cos2A2sin2A+sin2A2cos2A2sin2Asin2Acos2A

= 2(cos2Asin2A)+cos2A+sin2A2(cos2Asin2A)(sin2A+cos2A)

= 2cos2A+12cos2A1 = L.H.S


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