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Question
Without using tables, evaluate the following: cosec330° cos60° tan345° sin290° sec245° cot30°.
Solution
cosec330° cos60° tan345° sin290° sec245° cot30°.
sin30° = `(1)/(2)`
cosec30° = 2
cos60° = `(1)/(2)`
sec60° = 2
cos45° = `(1)/sqrt(2)`
sec45° = `sqrt(2)`
tan45° = 1
sin90° = 1
tan30° = `(1)/sqrt(3)`
⇒ cot30° = `sqrt(3)`
cosec330° cos60° tan345° sin290° sec245° cot30°
= `(2)^3(1/2)(1)^3(1)^2(sqrt(2))^2(sqrt(3))`
= `8 xx (1)/(2) xx 2 xx sqrt(3)`
= `8sqrt(3)`.
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