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CBSE Class 11-science Answered

show that   (3 + cot76 cot16 )/ (cot76 + cot 16 ) = tan46
Asked by ahuja8087 | 15 Mar, 2016, 05:04: PM
answered-by-expert Expert Answer
begin mathsize 12px style straight L. straight H. straight S. equals fraction numerator 3 plus cot 76 cot 16 over denominator cot 76 plus cot 16 end fraction equals fraction numerator 3 plus begin display style fraction numerator cos 76 cos 16 over denominator sin 76 sin 16 end fraction end style over denominator begin display style fraction numerator cos 76 over denominator sin 76 end fraction end style plus begin display style fraction numerator cos 16 over denominator sin 16 end fraction end style end fraction equals fraction numerator 3 sin 76 sin 16 plus cos 76 cos 16 over denominator cos 76 sin 16 plus sin 76 cos 16 end fraction equals fraction numerator 2 sin 76 sin 16 plus sin 76 sin 16 plus cos 76 cos 16 over denominator sin open parentheses 76 plus 16 close parentheses end fraction equals fraction numerator 2 sin open parentheses 46 plus 30 close parentheses sin open parentheses 46 minus 30 close parentheses plus cos open parentheses 76 minus 16 close parentheses over denominator sin 92 end fraction equals fraction numerator 2 open square brackets sin squared 46 minus sin squared 30 close square brackets plus cos 60 over denominator 2 sin 46 cos 46 end fraction equals fraction numerator 2 sin squared 46 minus begin display style 1 half end style plus begin display style 1 half end style over denominator 2 sin 46 cos 46 end fraction equals fraction numerator 2 sin squared 46 over denominator 2 sin 46 cos 46 end fraction equals fraction numerator sin 46 over denominator cos 46 end fraction equals tan 46 equals straight R. straight H. straight S. end style
Answered by satyajit samal | 16 Mar, 2016, 12:16: PM

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