Evaluate sin 30°+ tan45°-cosec60°/sec30°+cos60°+cot45°

Asked by ashleshathakur124 | 10th Feb, 2020, 09:39: PM

Expert Answer:

 
 
begin mathsize 16px style fraction numerator sin space 30 degree plus tan 45 degree minus cosec 60 degree over denominator sec space 30 degree plus cos 60 degree plus cot 45 degree end fraction
equals fraction numerator begin display style 1 half end style space plus 1 minus space begin display style fraction numerator 2 over denominator square root of 3 end fraction end style over denominator fraction numerator 2 over denominator square root of 3 end fraction plus begin display style 1 half end style plus 1 end fraction
equals fraction numerator square root of 3 space plus 2 square root of 3 minus 4 over denominator 4 plus square root of 3 plus 2 square root of 3 end fraction
equals fraction numerator 3 square root of 3 space minus space 4 over denominator 3 square root of 3 space plus 4 end root end fraction cross times fraction numerator 3 square root of 3 space minus space 4 over denominator 3 square root of 3 space minus space 4 end root end fraction
equals space fraction numerator 27 space minus space 12 square root of 3 space minus 12 square root of 3 plus space 16 space over denominator 27 minus 16 end fraction
equals fraction numerator 43 minus 24 square root of 3 space over denominator 11 end fraction end style

Answered by Yasmeen Khan | 11th Feb, 2020, 11:23: AM