Find the general solution for the equation

Question

2 sinx cosx =1

Answer 1

2sinxcosx =1

=> sin2x =1   since sin2x = 2sinxcosx

=> 2x = sin(pi/x)

=> 2x = (4n+1)*pi/2    {general solution of sinx = 1}

=> x = (4n+1)*pi/4

Comments

where n ∈ Z

and correction: line 3 should be

sin(2x) = sin(pi/2)

Answer 2

This is the same as sin(2x)=1, so 2x=π/2, 5π/2, 9π/2, ...

Therefore x=π/4, 5π/4, 9π/4, ...