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Question
Prove that:
`((tan60° + 1)/(tan 60° – 1))^2 = (1+ cos 30°) /(1– cos 30°) `
Solution
LHS = `((tan60°+ 1)/(tan 60° – 1))^2`
= `((sqrt3 +1)/(sqrt3 - 1))^2`
= `(sqrt3 +1)^2/(sqrt3 -1)^2`
= `((sqrt3)^2+(1)^2+2xxsqrt3xx1)/((sqrt3)^2+(1)^2-2xxsqrt3xx1)`
= `(3+1+2sqrt3)/(3+1-2sqrt3)`
= `(4 + 2sqrt3)/(4 -2sqrt3 )`
= `(2(2+sqrt3))/(2(2- sqrt3)`
= `(2+sqrt3)/(2-sqrt3)`
R.H.S
= `(1+ cos 30°) /(1- cos 30°)`
= `(1+sqrt3/2)/(1-sqrt3/2)`
= `((2 + sqrt3)/2)/((2 - sqrt3)/2)`
= `(2+sqrt3)/(2-sqrt3)`
L.H.S = R.H.S
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