IF cotA = ac^1/2 , cotB = (c/a)^1/2 , tanC = (c/a^3)^1/2 and c = a^2 + a + 1 .

Asked by Sanjay | 13th May, 2015, 12:45: AM

Expert Answer:

T h e space q u e s t i o n space y o u space h a v e space p o s t e d space i s space i n c o m p l e t e space a n d space i n c o r r e c t. T h e space c o r r e c t e d space q u e s t i o n space f o r space y o u r space q u e r y space i s space a s space f o l l o w s colon I f space c o t A equals open parentheses a c close parentheses to the power of 1 divided by 2 end exponent comma space c o t B equals open parentheses c divided by a close parentheses to the power of 1 divided by 2 end exponent comma space tan C equals open parentheses c divided by a cubed close parentheses to the power of 1 divided by 2 end exponent space a n d space c equals a squared plus a plus 1 comma space t h e n space p r o v e space t h a t space A plus B equals C.  S o l u t i o n colon I f space A plus B equals C comma space t h e n space c o t left parenthesis A plus B right parenthesis equals c o t C rightwards double arrow fraction numerator c o t A. c o t B minus 1 over denominator c o t A plus c o t B end fraction equals c o t C N o w space u sin g space t h e space v a l u e s space o f space c o t A comma space c o t B space a n d space tan space C thin space g i v e n space i n space t h e space q u e s t i o n comma space w e space g e t space fraction numerator open parentheses a c close parentheses to the power of 1 divided by 2 end exponent cross times open parentheses c divided by a close parentheses to the power of 1 divided by 2 end exponent minus 1 over denominator open parentheses a c close parentheses to the power of 1 divided by 2 end exponent plus open parentheses c divided by a close parentheses to the power of 1 divided by 2 end exponent end fraction equals open parentheses a cubed over c close parentheses to the power of 1 divided by 2 end exponent rightwards double arrow fraction numerator c minus 1 over denominator open parentheses a square root of c plus square root of c close parentheses divided by square root of a end fraction equals a to the power of 3 divided by 2 end exponent over c to the power of 1 divided by 2 end exponent rightwards double arrow fraction numerator square root of a over denominator square root of c end fraction open parentheses fraction numerator c minus 1 over denominator a plus 1 end fraction close parentheses equals a to the power of 3 divided by 2 end exponent over c to the power of 1 divided by 2 end exponent rightwards double arrow fraction numerator c minus 1 over denominator a plus 1 end fraction equals a rightwards double arrow c minus 1 equals a squared plus a rightwards double arrow c equals a squared plus a plus 1 w h i c h space i s space t r u e space a s space p e r space t h e space q u e s t i o n. space H e n c e comma space o u r space i n i t i a l space a s s u m p t i o n space t h a t space A plus B equals C space i s space t r u e. space H e n c e comma space p r o v e d.

Answered by satyajit samal | 13th May, 2015, 12:43: PM

Queries asked on Sunday & after 7pm from Monday to Saturday will be answered after 12pm the next working day.