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show that cotA-cosA/cotA+cosA=cosecA-1/cosecA+1
Asked by prabinbinu2001 | 25 Sep, 2016, 03:26: PM
answered-by-expert Expert Answer
begin mathsize 20px style W e space k n o w space t h a t space C o t A equals fraction numerator C o s space A over denominator S i n A end fraction S u b s i t u t e space t h e space v a l u e space o f space C o t A equals fraction numerator C o s space A over denominator S i n A end fraction space i n space t h e space L H S space o f space t h e space g i v e n space E q u a t i o n W e space g e t comma fraction numerator C o t space A space minus space C o s space A over denominator C o t space A space plus space C o s A end fraction equals space fraction numerator fraction numerator C o s space A over denominator S i n A end fraction minus C o s space A over denominator fraction numerator C o s space A over denominator S i n A end fraction plus C o s space A end fraction equals fraction numerator C o s space A open parentheses begin display style fraction numerator 1 over denominator S i n space A end fraction end style minus 1 close parentheses over denominator C o s space A open parentheses fraction numerator 1 over denominator S i n space A end fraction plus 1 close parentheses end fraction space space open square brackets T a k i n g space C o s space A space c o m m o n space f r o m space b o t h space t h e space s i d e s close square brackets space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space fraction numerator open parentheses fraction numerator 1 over denominator S i n space A end fraction minus 1 close parentheses over denominator open parentheses fraction numerator 1 over denominator S i n space A end fraction plus 1 close parentheses end fraction space space space open square brackets C a n c e l l i n g space C o s space A space f r o m space b o t h space t h e space s i d e s close square brackets space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals fraction numerator cos e c space A minus 1 space over denominator cos e c space A plus 1 end fraction space space space open square brackets fraction numerator 1 over denominator S i n space A end fraction equals C o s e c A close square brackets space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space R H S H e n c e space L H S space equals space R H S end style
Answered by Tripti Agrawal | 26 Sep, 2016, 11:34: AM

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CBSE 10 - Maths
the poles AB and CD of different heights are standing vertically on the ground level from a point P on the line joining the foots of the pole on the level of ground the angle of elevation to the top of the pole are founded to be complementary the of the CD and the distance PD 20√3m and 20m respectively if the BP is 10m then find the length of AB and the distance AC between the tpo of the poles
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