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Question
Prove that `cot^2 pi/6 + cosec (5pi)/6 + 3 tan^2 pi/6 = 6`
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Solution
Left side = `cot^2 pi/6 + cosec (5pi)/6 + 3 tan^2 pi/6`
= `(sqrt3)^2 + cosec (pi-pi/6) + 3 (1/sqrt3)^2`
`(∴ cot pi/6 = sqrt3, tan pi/6 = 1/sqrt3)`
= 3 + cosec `pi/6+ 3 xx 1/3`
[∵cosec `(pi-θ)= cosec θ`]
= 3 + 2 + 1 = 6 = Right Side.
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