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Question
Without using tables, evaluate the following sec45° sin45° - sin30° sec60°.
Solution
sec45° sin45° - sin30° sec60°.
cos45° = `(1)/sqrt(2)`
⇒ sec45° = `sqrt(2)`
sin45° = `(1)/sqrt(2)`
sin30° = `(1)/(2)`
cos60° = `(1)/(2)`
⇒ sec60° = 2
sec45° sin45° - sin30° sec60°
= `sqrt(2) xx (1)/sqrt(2) - (1)/sqrt(2) xx 2`
= 1 - 1
= 0.
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