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=pi+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 = π + 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 = π + 2 πn

Solve

2 x - x = π + 2 πn : x = π + 2 πn

x = π + 2 πn

2 tan^{2} (x) = - 3 + 3 sec (x)

5 csc^{2} (\frac{θ}{2}) - 16 = 0

sin (3 x) sin (x) = 0, 0 \leq x \leq 2 π

2 tan (x) = 3 csc (x)

sin (t) = \frac{120}{500} sin (11 0^{\circ})

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=pi+2pin