solve the following equation for all values of x: sin^2x+sinxcosx



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solve the following equation for all values of x: sin2x+sinxcosx

Answer & Explanation



Skilled2021-03-09Added 102 answers

sin(x)(sin(x)+cos(x)). If this expression equals zero, sin(x)=0 or sin(x)=cos(x), so tan(x)=1.
Solutions: sin(x)=0:x=n(π),tan(x)=1:x=(4n1)π4 where n is an integer. x is in radians. To convert to degrees put (π)=180: 0, 180, 360, ..., 135, 315, ... for example.
cos(2x)=12sin2(x), so sin2(x)=1cos(2x)2
sin(2x)=2sin(x)cos(x), so sin(x)cos(x)=(12)sin(2x)
sin2(x)+sin(x)cos(x)=(12)(1cos(2x)+sin(2x)). Above solutions apply.

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