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Question
Without using tables, find the value of the following: `(sin30°)/(sin45°) + (tan45°)/(sec60°) - (sin60°)/(cot45°) - (cos30°)/(sin90°)`
Solution
`(sin30°)/(sin45°) + (tan45°)/(sec60°) - (sin60°)/(cot45°) - (cos30°)/(sin90°)`
= `(1/2)/(1/sqrt(2)) + (1)/(2) - (sqrt(3)/2)/(1) - (sqrt(3)/2)/(1)`
= `sqrt(2)/(2) + (1)/(2) - sqrt(3)/(2) - sqrt(3)/(2)`
= `(sqrt(2) + 1 - 2sqrt(3))/(2)`.
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