2sinA=2-cosA,1-sin^2(A)=4sin^2(A)-8sinA+4,5sin^2(A)-8sinA+3=0,sinA=(8±2)/10,sinA=1 or 3/5

Thanks a tonne sir for the solution, I got an idea but could not understand how did you reach the equation SinA=(8+2)/10 from 5sin^2A-8sinA+3.

wont simple factorization by grouping do?  Or it is the latest formulae to obtain the value, if so, kindly illustrate the formulae.

  5 sin²A - 8 sinA + 3 { in the form of ax²+bx+c=0 }

 which has the roots

so sinA= -(-8) + (8²-4.5.3)^1/2           -(-8) - (8²-4.5.3)^1/2 

                     ---------------------------------------  or ------------------------ 

                               2(5)                               2(5)

           =  {8 + 2}/10 or  {8-2}/10

Thanx for the answer sir but can you please elaborate the 1st three steps, i will be really gratefull.

Thanx..