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Question
Evaluate: `5/(cot^2 30^circ) + 1/(sin^2 60^circ) - cot^2 45^circ + 2 sin^2 90^circ`.
Solution
`5/(cot^2 30^circ) + 1/(sin^2 60^circ) - cot^2 45^circ + 2 sin^2 90^circ`
= `5/(sqrt(3))^2 + 1/(sqrt(3)/2)^2 - (1)^2 + 2 xx (1)^2`
= `5/3 + 4/3 - 1 + 2`
= `9/3 + 1`
= 4
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