Paragraph: Given that x+ x+ x+ x+ x+ cosec x=7 Question: The given equation can be reduced to

Step-by-step solution

x+ x+ x+ x+ x+ cosec x=7( x+ x)+ ( x x + x x )+ ( 1 x + 1 x )=7( x+ x)+ 1 x x + x+ x x x =7( x+ x) (1+ 1 x x )+ 1 x x =7 ( x+ x)( x x+1)+1 x x =7( x+ x)( x x+1)+1=7 x x( x+ x)( x x+1)=7 x x-1 Squaring both sides aligned (1+ 2 x) ( 1 4 ^2 2 x+1+ 2 x ) & & = 49 4 ^2 2 x+1-7 2 x aligned aligned (1+ 2 x) ( ^2 2 x+4 2 x+4 ) & & =49 ^2 2 x-28 2 x aligned array r ^2 2 x+4 2 x+4+ ^3 2 x+4 ^2 2 x+4 2 x =49 ^2 2 x-28 2 x+4 array ^3 2 x-44 ^2 2 x+36 2 x=0 2 x ( ^2 2 x-44 2 x+36 )=0 ^2 2 x-44 2 x+36=0