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

The general solution for cos^2(x)+2sin(x)cos(x)-sin^2(x)=0 is x=pin-pi/8 ,x=pin+pi/2-pi/8

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

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

x = πn - \frac{π}{8}, x = πn + \frac{π}{2} - \frac{π}{8}

Solution steps

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

Rewrite using trig identities

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

Rewrite using trig identities

2 sin (2 x + \frac{π}{4}) = 0

Divide both sides by

2

sin (2 x + \frac{π}{4}) = 0

General solutions for

sin (2 x + \frac{π}{4}) = 0

2 x + \frac{π}{4} = 0 + 2 πn, 2 x + \frac{π}{4} = π + 2 πn

Solve

2 x + \frac{π}{4} = 0 + 2 πn : x = πn - \frac{π}{8}

Solve

2 x + \frac{π}{4} = π + 2 πn : x = πn + \frac{π}{2} - \frac{π}{8}

x = πn - \frac{π}{8}, x = πn + \frac{π}{2} - \frac{π}{8}

4 sin (2 θ) = 0

cos (4 θ) = \frac{1}{2}

1 - cos (\frac{x}{2}) = cos (\frac{x}{2})

2 cos^{2} (θ) + 2 cos (θ) - 1 = 0

- 2 sin (- 3 x) - 1 = 0

What is the general solution for cos^2(x)+2sin(x)cos(x)-sin^2(x)=0 ?
The general solution for cos^2(x)+2sin(x)cos(x)-sin^2(x)=0 is x=pin-pi/8 ,x=pin+pi/2-pi/8