If m tan(A-30 degrees) = n tan(A+120degrees),show that cos2A = m+n/2(m-n)

Asked by Sanjay | 13th May, 2015, 02:07: PM

Expert Answer:

$m tan open parentheses A minus 30 to the power of o close parentheses equals n tan open parentheses A plus 120 to the power of o close parentheses rightwards double arrow m over n equals fraction numerator tan open parentheses 90 to the power of o plus A plus 30 to the power of 0 close parentheses over denominator tan open parentheses A minus 30 to the power of o close parentheses end fraction rightwards double arrow m over n equals fraction numerator negative c o t open parentheses A plus 30 to the power of 0 close parentheses over denominator tan open parentheses A minus 30 to the power of o close parentheses end fraction rightwards double arrow m over n equals fraction numerator negative 1 over denominator tan open parentheses A plus 30 to the power of 0 close parentheses tan open parentheses A minus 30 to the power of o close parentheses end fraction rightwards double arrow m over n equals fraction numerator negative open parentheses 1 minus tan squared A tan squared 30 to the power of o close parentheses over denominator tan squared A minus tan squared 30 to the power of o end fraction space open parentheses U s e space tan left parenthesis A plus B right parenthesis space a n d space tan left parenthesis A minus B right parenthesis space f o r m u l a e close parentheses rightwards double arrow m over n equals fraction numerator begin display style fraction numerator tan squared A over denominator 3 end fraction end style minus 1 over denominator tan squared A minus begin display style 1 third end style end fraction rightwards double arrow m over n equals fraction numerator tan squared A minus 3 over denominator 3 tan squared A minus 1 end fraction rightwards double arrow fraction numerator m plus n over denominator m minus n end fraction equals fraction numerator 4 tan squared A minus 4 over denominator negative 2 tan squared A minus 2 end fraction rightwards double arrow fraction numerator m plus n over denominator m minus n end fraction equals 2 open parentheses fraction numerator 1 minus tan squared A over denominator 1 plus tan squared A end fraction close parentheses rightwards double arrow fraction numerator m plus n over denominator 2 open parentheses m minus n close parentheses end fraction equals cos 2 A$

Answered by satyajit samal | 13th May, 2015, 06:49: PM

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