What is the general solution for cos(2x)cos(x)+sin(2x)sin(x)=1 ?

The general solution for cos(2x)cos(x)+sin(2x)sin(x)=1 is x=2pin

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

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

x = 2 πn

Solution steps

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

Rewrite using trig identities

cos (2 x - x) = 1

General solutions for

cos (2 x - x) = 1

2 x - x = 0 + 2 πn

Solve

2 x - x = 0 + 2 πn : x = 2 πn

x = 2 πn

cos (2 θ) + 10 sin^{2} (θ) = 7

4 cos (2 t) + 1 = 3

cos (2 x) - cos (x) = - 1

cos (x + \frac{π}{4}) - cos (x - \frac{π}{4}) = 1

y, x = cos (y)

What is the general solution for cos(2x)cos(x)+sin(2x)sin(x)=1 ?
The general solution for cos(2x)cos(x)+sin(2x)sin(x)=1 is x=2pin