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Question
Without using tables, evaluate the following: cosec245° sec230° - sin230° - 4cot245° + sec260°.
Solution
cosec245° sec230° - sin230° - 4cot245° + sec260°.
sin45° = `(1)/sqrt(2)`
cosec45° = `sqrt(2)/(1)`
sin30° = `(1)/(2)` = cos60°
sec60° = 2
cos30° = `sqrt(3)/(2)`
sec30° = `(2)/sqrt(3)`
tan45° = 1
cot45° = 1
cosec245° sec230° - sin230° - 4cot245° + sec260°
= `(sqrt(2)/1)^2 (2/sqrt(3))^2 - (1/2)^2 - 4(1)^2 + (2)^2`
= `2 xx (4)/(3) - (1)/(4) - 4 + 4`
= `(8)/(3) - (1)/(4)`
= `(32 - 3)/(12)`
= `(29)/(12)`.
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