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

The general solution for -sin(2x)sin(x)+cos(2x)cos(x)=0 is x= pi/6+(2pin)/3 ,x= pi/2+(2pin)/3

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

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

x = \frac{π}{6} + \frac{2 πn}{3}, x = \frac{π}{2} + \frac{2 πn}{3}

Solution steps

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

Rewrite using trig identities

cos (2 x + x) = 0

General solutions for

cos (2 x + x) = 0

2 x + x = \frac{π}{2} + 2 πn, 2 x + x = \frac{3 π}{2} + 2 πn

Solve

2 x + x = \frac{π}{2} + 2 πn : x = \frac{π}{6} + \frac{2 πn}{3}

Solve

2 x + x = \frac{3 π}{2} + 2 πn : x = \frac{π}{2} + \frac{2 πn}{3}

x = \frac{π}{6} + \frac{2 πn}{3}, x = \frac{π}{2} + \frac{2 πn}{3}

sin (2 x) + cos (2 x) - 1 = 0

4 tan (x) sin^{2} (x) + 3 = 4 sin^{2} (x) + 3 tan (x)

tan (a) = 0.384

cos (b) = \frac{38}{70}

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

What is the general solution for -sin(2x)sin(x)+cos(2x)cos(x)=0 ?
The general solution for -sin(2x)sin(x)+cos(2x)cos(x)=0 is x= pi/6+(2pin)/3 ,x= pi/2+(2pin)/3