Without using trigonometric tables, evaluate:
$2 fraction numerator sin space 43 degree over denominator cos space 47 degree end fraction minus fraction numerator cot space 30 degree over denominator tan space 60 degree end fraction minus square root of 2 space sin space 45 degree$

0
2
4
1

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Solution

2 space fraction numerator sin space 43 degree over denominator cos space 47 degree end fraction minus fraction numerator cot space 30 degree over denominator tan space 60 degree end fraction minus square root of 2 space sin space 45 degree comma space space space 2 fraction numerator sin left parenthesis 90 degree minus 47 degree right parenthesis over denominator cos space 47 degree end fraction minus fraction numerator cot space left parenthesis 90 degree minus 60 degree right parenthesis over denominator tan space 60 degree end fraction minus square root of 2 cross times 1 half space rightwards double arrow space space space 2. space fraction numerator cos space 47 degree over denominator cos space 47 degree end fraction minus fraction numerator tan space 60 degree over denominator tan space 60 degree end fraction minus 1 space equals space 2 minus 1 minus 1 space equals space 0

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