If ( (x+1)² x³+x = A x + B x+C x²+1 ), then ( cosec ⁻¹ ( 1 A )+ ⁻¹ ( 1 B )+ ⁻¹ C= )

Step-by-step solution

Given that ( (x+1)² x³+x = A x + B x+C x²+1 (1) ) [ array l x²+1+2 x x (x²+1 ) = A x + B x+C (x²+1 ) x²+1 (x²+1 ) + 2 x (x²+1 ) = A + B x+C (x²+1 ) 1 + 2 ²+1 = A + B x+C (x²+1 ) array ] Comparing the coefficients, we have, [ A=1, B=0, C=2 ] Now, [ array l cosec ⁻¹ ( 1 A )+ ⁻¹ ( 1 B )+ ⁻¹ C cosec ⁻¹(1)+ ⁻¹ ( 1 0 )+ ⁻¹(2) = 2 +0+ 3 = 5 6 array ]