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Question
Evaluate the following:
`(sin 30° + tan 45° – cosec 60°)/(sec 30° + cos 60° + cot 45°)`
Solution
`(sin 30° + tan 45° – cosec 60°)/(sec 30° + cos 60° + cot 45°)`
= `(1/2+1-2/sqrt3)/(2/sqrt3+1/2+1)`
= `((3/2-2/sqrt3)/(3/2+2/sqrt3))`
= `((3sqrt3 - 4)/(2sqrt3))/((4 + 3sqrt3)/(2sqrt3))`
= `(3sqrt3-4)/(3sqrt3+4)`
= `((3sqrt3-4)(3sqrt3-4))/((3sqrt3+4)(3sqrt3-4))`
= `((3sqrt3-4)^2)/((3sqrt3)^2 -(4)^2)`
= `(27+16-24sqrt3)/(27-16)`
= `(43-24sqrt3)/11`
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