What is the general solution for 2sin^2(x)-sin(x)cos(x)-cos^2(x)=0 ?

The general solution for 2sin^2(x)-sin(x)cos(x)-cos^2(x)=0 is x=-0.46364…+pin,x= pi/4+pin

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2sin^2(x)-sin(x)cos(x)-cos^2(x)=0

2 sin^{2} (x) - sin (x) cos (x) - cos^{2} (x) = 0

x = - 0.46364 \dots + πn, x = \frac{π}{4} + πn

Solution steps

2 sin^{2} (x) - sin (x) cos (x) - cos^{2} (x) = 0

Factor

2 sin^{2} (x) - sin (x) cos (x) - cos^{2} (x) : (2 sin (x) + cos (x)) (sin (x) - cos (x))

(2 sin (x) + cos (x)) (sin (x) - cos (x)) = 0

Solving each part separately

2 sin (x) + cos (x) = 0 or sin (x) - cos (x) = 0

2 sin (x) + cos (x) = 0 : x = arctan (- \frac{1}{2}) + πn

sin (x) - cos (x) = 0 : x = \frac{π}{4} + πn

Combine all the solutions

x = arctan (- \frac{1}{2}) + πn, x = \frac{π}{4} + πn

Show solutions in decimal form

x = - 0.46364 \dots + πn, x = \frac{π}{4} + πn

cos^{4} (a) + cos^{2} (a) + sin^{2} (a) + sin^{2} (a) = 1

22 sin (x) + sec (x) = 0

cos (θ) = \frac{- 2}{( 30 + ( 7 ) )}

cos^{3} (x) - 2 sin (x) - 0.7 = 0

cos^{2} (x) - sin^{2} (x) = sec^{2} (x) - csc^{2} (x)

What is the general solution for 2sin^2(x)-sin(x)cos(x)-cos^2(x)=0 ?
The general solution for 2sin^2(x)-sin(x)cos(x)-cos^2(x)=0 is x=-0.46364…+pin,x= pi/4+pin