4sinxcosx-1=2(sinx-cosx) find x
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4sinx*cosx -1 = 2(sinx-cosx)
We will expand the brackets.
==> 4sinxcosx -1 = 2sinx -2cosx
Now we will move all terms to the left side.
==> 2cosx -2sinx +4sinxcosx -1 = 0
==> 2cosx +4sinxcosx - 2sinx -1 = 0
Now we will factor 2cosx and -1.
==> 2cosx( 1+ 2sinx) -( 2sinx+1) = 0
Now we will factor (2sinx+1)
==> (2sinx+1) *(2cosx -1) = 0
==> 2sinx = -1 ==> sinx = -1/2 ==>
x= pi+pi/6 = 7pi/6 + 2npi
x = 2pi - pi/6 = 11pi/6 + 2npi
==> 2cosx -1 = 0 ==> cosx = 1/2
==> x = pi/3 + 2npi
==> x = 2pi - pi/3 = 5pi/3 + 2npi
==> x = { 7pi/6 + 2npi , 11pi/6 + 2npi, pi/3 + 2npi , 5pi/3+ 2npi} n= 1, 2, 3, 4, .....
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