cosa=2cosb-1/2-cosb  find  tana/2cotb/2

Asked by ushha1971 | 6th Nov, 2014, 06:49: PM

Expert Answer:

G i v e n space t h a t space cos a equals fraction numerator 2 cos b minus 1 over denominator 2 minus cos b end fraction W e space k n o w space t h a t space cos a equals fraction numerator 1 minus tan squared begin display style a over 2 end style over denominator 1 plus tan squared begin display style a over 2 end style end fraction ; space cos b equals fraction numerator 1 minus tan squared begin display style b over 2 end style over denominator 1 plus tan squared begin display style b over 2 end style end fraction T h u s comma space w e space h a v e comma fraction numerator 1 minus tan squared begin display style a over 2 end style over denominator 1 plus tan squared begin display style a over 2 end style end fraction equals fraction numerator 2 cross times open parentheses fraction numerator 1 minus tan squared begin display style b over 2 end style over denominator 1 plus tan squared begin display style b over 2 end style end fraction close parentheses minus 1 over denominator 2 minus open parentheses fraction numerator 1 minus tan squared begin display style b over 2 end style over denominator 1 plus tan squared begin display style b over 2 end style end fraction close parentheses end fraction rightwards double arrow fraction numerator 1 minus tan squared begin display style a over 2 end style over denominator 1 plus tan squared begin display style a over 2 end style end fraction equals fraction numerator fraction numerator 2 minus 2 tan squared begin display style b over 2 end style over denominator 1 plus tan squared begin display style b over 2 end style end fraction minus 1 over denominator 2 minus open parentheses fraction numerator 1 minus tan squared begin display style b over 2 end style over denominator 1 plus tan squared begin display style b over 2 end style end fraction close parentheses end fraction rightwards double arrow fraction numerator 1 minus tan squared begin display style a over 2 end style over denominator 1 plus tan squared begin display style a over 2 end style end fraction equals fraction numerator 2 minus 2 tan squared b over 2 minus 1 minus tan squared b over 2 over denominator 2 plus 2 tan squared b over 2 minus 1 plus tan squared b over 2 end fraction rightwards double arrow fraction numerator 1 minus tan squared begin display style a over 2 end style over denominator 1 plus tan squared begin display style a over 2 end style end fraction equals fraction numerator 1 minus 3 tan squared b over 2 over denominator 1 plus 3 tan squared b over 2 end fraction rightwards double arrow open parentheses 1 minus tan squared a over 2 close parentheses open parentheses 1 plus 3 tan squared b over 2 close parentheses equals open parentheses 1 plus tan squared a over 2 close parentheses open parentheses 1 minus 3 tan squared b over 2 close parentheses rightwards double arrow 1 plus 3 tan squared b over 2 minus tan squared a over 2 minus 3 tan squared a over 2 tan squared b over 2 equals 1 minus 3 tan squared b over 2 plus tan squared a over 2 minus 3 tan squared a over 2 tan squared b over 2 rightwards double arrow 6 tan squared b over 2 minus 2 tan squared a over 2 equals 0 rightwards double arrow 3 tan squared b over 2 equals tan squared a over 2 rightwards double arrow fraction numerator tan squared a over 2 over denominator tan squared b over 2 end fraction equals 3 rightwards double arrow fraction numerator tan a over 2 over denominator tan b over 2 end fraction equals square root of 3 rightwards double arrow tan a over 2 cross times c o t b over 2 equals square root of 3

Answered by Vimala Ramamurthy | 7th Nov, 2014, 09:15: AM