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CBSE Class 11-science Answered

sin alpha+sin beta = m and cos alpha+cos beta=n
find tan (alpha-beta)/2
Asked by 23-08-2000 | 20 Jul, 2015, 08:36: PM
answered-by-expert Expert Answer
sin alpha plus sin beta equals m rightwards double arrow sin squared alpha plus s i n squared beta plus 2 s i n alpha s i n beta equals m squared.. left parenthesis 1 right parenthesis cos alpha plus cos beta equals n rightwards double arrow cos squared alpha plus cos squared beta plus 2 cos alpha cos beta equals n squared.. left parenthesis 2 right parenthesis A d d i n g space left parenthesis 1 right parenthesis space a n d space left parenthesis 2 right parenthesis comma space w e space g e t s i n squared alpha plus c o s squared alpha plus s i n squared beta plus c o s squared beta plus 2 s i n alpha s i n beta plus 2 c o s alpha c o s beta equals m squared plus n squared rightwards double arrow 1 plus 1 plus 2 open parentheses c o s alpha c o s beta plus s i n alpha s i n beta close parentheses equals m squared plus n squared rightwards double arrow cos open parentheses alpha minus beta close parentheses equals fraction numerator m squared plus n squared minus 2 over denominator 2 end fraction.... left parenthesis 3 right parenthesis tan squared open parentheses fraction numerator alpha minus beta over denominator 2 end fraction close parentheses equals fraction numerator s i n squared open parentheses fraction numerator alpha minus beta over denominator 2 end fraction close parentheses over denominator cos squared open parentheses fraction numerator alpha minus beta over denominator 2 end fraction close parentheses end fraction equals fraction numerator 2 s i n squared open parentheses fraction numerator alpha minus beta over denominator 2 end fraction close parentheses over denominator 2 c o s squared open parentheses fraction numerator alpha minus beta over denominator 2 end fraction close parentheses end fraction equals fraction numerator 1 minus c o s open parentheses alpha minus beta close parentheses over denominator 1 plus c o s open parentheses alpha minus beta close parentheses end fraction equals fraction numerator 1 minus fraction numerator m squared plus n squared minus 2 over denominator 2 end fraction over denominator 1 plus fraction numerator m squared plus n squared minus 2 over denominator 2 end fraction end fraction rightwards double arrow t a n squared open parentheses fraction numerator alpha minus beta over denominator 2 end fraction close parentheses equals fraction numerator negative m squared minus n squared plus 4 over denominator m squared plus n squared end fraction rightwards double arrow t a n open parentheses fraction numerator alpha minus beta over denominator 2 end fraction close parentheses equals plus-or-minus square root of fraction numerator 4 minus m squared minus n squared over denominator m squared plus n squared end fraction end root
Answered by satyajit samal | 21 Jul, 2015, 11:40: AM

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