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Without using trigonometric tables, evaluate the following:2/3 cosec258° - 2/3 cot58°tan32° - 5/3 tan13°tan37°tan 45°tan 53°tan 77° |
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Answer» 2/3cosec258° - 2/3cot58°tan32° - 5/3 tan13°tan37°tan 45°tan 53°tan 77° = 2/3(cosec258°- cot 58°tan32°) - 5/3 tan13°tan(90° - 13°) tan 37°tan(90° - 37°)(tan45°) = 2/3[cosec258°- cot 58°tan(90°- 58°)] - 5/3 tan13°cot13°tan37°cot37°(1) = 2/3(cosec258°- cot58°tan58°)- 5/3tan13°\(\frac{1}{tan13°}\)tan37°\(\frac{1}{tan37°}\) = 2/3(cosec258°- cot258°- 5/3 = 2/3 - 5/3 = - 1 Hence proved |
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