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Show that : tan (60^0 + A). Tan (60^0 -A...

Show that : tan (60^0 + A). Tan (60^0 -A) = (2 cos 2A+1)/(2cos 2A-1)`

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RHS `=tan(60^(@)+A)tan(60^(@)-A)`
`=((tan60^(@)+tanA)/(1-tan60^(@)tanA))((tan60^(@)-tanA)/(1+tan60^(@)tanA))=((sqrt(3)+tanA)/(1-sqrt(3)tanA))((sqrt(3)-tanA)/(1+sqrt(3)tanA))`
`=(3-tan^(2)A)/(1-3tan^(2)A)=(3-(sin^(2)A)/( cos^(2)A))/(1-3(sin^(2)A)/(cos^(2)A))=(3cos^(2)A-sin^(2)A)/(cos^(2)A-3sin^(2)A)=(2cos^(2)A+cos^(2)A-2 sin^(2)A+sin^(2)A)/(2 cos^(2)A-2sin^(2)A-sin^(3)A-cos^(2)A)`
`=(2(cos^(2)A-sin^(2)A)+cos^(2)A+sin^(2)A)/(2(cos^(2)A-sin^(2)A)-(sin^(2)A+cos^(2)A))=(2cos2A+1)/(2cos2A-1)=LHS`
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