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Question
Without using tables, find the value of the following: `(4)/(cot^2 30°) + (1)/(sin^2 60°) - cos^2 45°`
Solution
`(4)/(cot^2 30°) + (1)/(sin^2 60°) - cos^2 45°`
= `(4)/(sqrt(3))^2 + 1/(sqrt3/2)^2 - (1/sqrt(2))^2`
= `(4)/(3) + (1)/(3/4) - (1)/(2)`
= `(4)/(3) + (4)/(3) - (1)/(2)`
= `(8 + 8 -3)/(6)`
= `(13)/(6)`.
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