Maths-
General
Easy

Question

The value of fraction numerator 3 plus cot 76 to the power of ring operator cot 16 to the power of ring operator over denominator cot 76 to the power of ring operator plus cot 16 to the power of ring operator end fraction is

  1. tan44°
  2. cot invisible function application 46 to the power of ring operator
  3. tan invisible function application 2 to the power of ring operator
  4. tan invisible function application 46 to the power of ring operator

The correct answer is: tan invisible function application 46 to the power of ring operator


    fraction numerator 3 plus cot 76 to the power of ring operator cot 16 to the power of ring operator over denominator cot 76 to the power of ring operator plus cot 16 to the power of ring operator end fraction
equals fraction numerator 3 plus begin display style fraction numerator cos 76 to the power of ring operator cos 16 to the power of ring operator over denominator sin 76 degree sin 16 degree end fraction end style over denominator begin display style fraction numerator cos 76 to the power of ring operator over denominator sin 76 degree end fraction end style plus begin display style fraction numerator cos 16 to the power of ring operator over denominator sin 16 degree end fraction end style end fraction
equals fraction numerator fraction numerator 3 sin 76 degree sin 16 degree plus cos 76 to the power of ring operator cos 16 to the power of ring operator over denominator sin 76 degree sin 16 degree end fraction over denominator begin display style fraction numerator cos 76 to the power of ring operator sin 16 degree plus cos 16 to the power of ring operator sin 76 degree over denominator sin 76 degree sin 16 degree end fraction end style end fraction
equals fraction numerator 3 sin 76 degree sin 16 degree plus cos 76 to the power of ring operator cos 16 to the power of ring operator over denominator begin display style cos 76 to the power of ring operator sin 16 degree plus cos 16 to the power of ring operator sin 76 degree end style end fraction
equals fraction numerator 2 sin 76 degree sin 16 degree plus open parentheses sin 76 degree sin 16 degree plus cos 76 to the power of ring operator cos 16 to the power of ring operator close parentheses over denominator begin display style cos 76 to the power of ring operator sin 16 degree plus cos 16 to the power of ring operator sin 76 degree end style end fraction
open parentheses because sin A sin B plus cos A cos B equals C o s open parentheses A minus B close parentheses space a n d space cos A sin B plus cos A sin B equals sin open parentheses A plus B close parentheses close parentheses
equals fraction numerator 2 sin 76 degree sin 16 degree plus open parentheses cos open parentheses 76 degree minus 16 degree close parentheses close parentheses over denominator begin display style sin open parentheses 76 degree plus 16 degree close parentheses end style end fraction
equals fraction numerator 2 sin 76 degree sin 16 degree plus open parentheses cos open parentheses 60 degree close parentheses close parentheses over denominator begin display style sin open parentheses 92 degree close parentheses end style end fraction
open parentheses because 2 sin A sin B equals cos open parentheses A minus B close parentheses minus cos open parentheses A plus B close parentheses close parentheses
equals fraction numerator cos open parentheses 76 degree minus 16 degree close parentheses minus cos open parentheses 76 degree plus 16 degree close parentheses plus open parentheses cos open parentheses 60 degree close parentheses close parentheses over denominator begin display style sin open parentheses 92 degree close parentheses end style end fraction
equals fraction numerator cos open parentheses 60 degree close parentheses minus cos open parentheses 92 degree close parentheses plus open parentheses cos open parentheses 60 degree close parentheses close parentheses over denominator begin display style sin open parentheses 92 degree close parentheses end style end fraction
equals fraction numerator 1 minus cos open parentheses 92 degree close parentheses over denominator begin display style sin open parentheses 92 degree close parentheses end style end fraction
open parentheses because 1 minus cos 2 A equals 2 sin squared A space a n d space sin 2 A equals 2 sin A cos A close parentheses
equals fraction numerator 2 sin squared 46 degree over denominator 2 sin 46 degree cos 46 degree end fraction
equals fraction numerator sin 46 degree over denominator cos 46 degree end fraction
equals tan 46 degree

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