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\frac { \operatorname { cos } 10 ^ { \circ } + \operatorname { sin } 20 ^ { \circ } } { \operatorname { cos } 20 ^ { \circ } - \operatorname { sin } 10 ^ { \circ } } ? |
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Answer» (cos10° + sin20°) / (cos20° - sin10°) = tan60° * (cos60°/sin60°) * [(cos10° + sin20°) / (cos20° - sin10°)] = tan60° * [(2cos60° cos10° + 2cos60° sin20°) / (2sin60°cos20° - 2sin60° sin10°)] = √3 * [(cos70° + cos50° + sin80° - sin40°) / (sin80° + sin40° - cos50° + cos70°)] = √3 * [(cos70° + cos50° + sin80° - cos50°) / (sin80° + cos50° - cos50° + cos70°)]{sin40° = cos50° sin(90-A)=cosA} = √3 * [(cos70° + sin80°) / (sin80° + cos70°)]= √3 |
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