solve the following equation for all values of x: sin2x+sin⁡xcos⁡x

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solve the following equation for all values of x:   sin2x+sin⁡xcos⁡x

SoosteethicU · Accepted Answer

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=(4n−1)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)=1−2sin2(x), so sin2(x)=1−cos⁡(2x)2  sin⁡(2x)=2sin⁡(x)cos⁡(x), so sin⁡(x)cos⁡(x)=(12)sin⁡(2x)  sin2(x)+sin⁡(x)cos⁡(x)=(12)(1−cos⁡(2x)+sin⁡(2x)). Above solutions apply.

solve the following equation for all values of x: sin2x+sin⁡xcos⁡x

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