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Question
Without using tables, evaluate the following: sec30° cosec60° + cos60° sin30°.
Solution
sec30° cosec60° + cos60° sin30°.
cos30° = `sqrt(3)/(2)`
⇒ sec30° = `(2)/sqrt(3)`
sin60° = `sqrt(3)/(2)`
⇒ cosec60° = `(2)/sqrt(3)`
cos60° = `(1)/(2) , sin30° = (1)/(2)`
sec30° cosec60° + cos60° sin30°
= `(2)/sqrt(3) xx (2)/sqrt(3) + (1)/(2) xx (1)/(2)`
= `(4)/(3) + (1)/(4)`
= `(16 + 3)/(12)`
= `(19)/(12)`.
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