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Question
Without using table, find the value of the following: `(tan^2 60° + 4cos^2 45° + 3sec^2 30° + 5cos90°)/(cosec30° + sec60° - cot^2 30°)`
Solution
`(tan^2 60° + 4cos^2 45° + 3sec^2 30° + 5cos90°)/(cosec30° + sec60° - cot^2 30°)`
= `((sqrt(3))^2 + 4 xx (1/sqrt(2))^2 + 3 xx (2/sqrt(3))^2 + 5 xx 0)/(2 + 2 - (sqrt(3))^2`
= `(3 + 4 xx (1)/(2) + 3 xx (4)/(3) + 0)/(2 + 2 - 3)`
= `(3 + 2 + 4)/(4 - 3)`
= 9.
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