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प्रश्न
Prove that: `((cot30° + 1)/(cot30° -1))^2 = (sec30° + 1)/(sec30° - 1)`
उत्तर
L.H.S. = `((cot30° + 1)/(cot30° -1))^2`
= `((sqrt(3) + 1)/(sqrt(3) - 1))^2`
= `((sqrt(3) + 1)/(sqrt(3) - 1) xx (sqrt(3) + 1)/(sqrt(3) + 1))^2`
= `((sqrt(3))^2 + (1)^2 + 2sqrt(3))/((sqrt(3))^2 + (1)^2 - 2sqrt(3)`
= `(3 + 1 + 2sqrt(3))/(3 + 1 - 2sqrt(3)`
= `(4 + 2sqrt(3))/(4 - 2sqrt(3)`
= `(2(2 + sqrt(3)))/(2(2 - sqrt(3))`
= `(2 + sqrt(3))/(2 - sqrt(3)`
= `(2/sqrt(3) + 1)/(2/sqrt(3) - 1)`
= `(sec30° + 1)/(sec30° - 1)`
= R.H.S.
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