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Question
Without using tables, evaluate the following: sin230° cos245° + 4tan230° + sin290° + cos20°
Solution
sin230° cos245° + 4tan230° + sin290° + cos20°
sin30° = `(1)/(2)`
cos45° = `(1)/sqrt(2)`
tan30° = `(1)/sqrt(3)`
sin90° = 1
cos0° = 1
sin230° cos245° + 4tan230° + sin290° + cos20°
= `(1/2)^2 (1/sqrt(2))^2 + 4(1/sqrt(3))^2 + 1 + 1`
= `(1)/(4) xx (1)/(2) + (4)/(3) + 2`
= `(1)/(8) + (4)/(3) + 2`
= `(3 + 32 + 48)/(24)`
= `(83)/(24)`.
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