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Homework Statement
The number of solutions of the equation sin2x –2cosx + 4sinx = 4 in the interval [0, 5π] is what?
Homework Equations
sin2x=2sinxcosx
The Attempt at a Solution
sin2x-2cosx+4sinx=4
⇒2sinxcosx-2cosx+4sinx=4
⇒sinxcosx-cosx+2sinx=2
⇒cosx (sinx-1)=2-2sinx
⇒cosx (sinx-1)=2 (1-sinx)
⇒cosx (sinx-1)= -2 (sinx-1)
⇒cosx = -2
∴ There is no solution