What is the general solution for cos(2x)-2sin(x)=1,0<x<= 360 ?

The general solution for cos(2x)-2sin(x)=1,0<x<= 360 is x=270,x=180,x=360

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cos(2x)-2sin(x)=1,0<x<= 360

cos (2 x) - 2 sin (x) = 1, 0^{\circ} < x \leq 36 0^{\circ}

x = 27 0^{\circ}, x = 18 0^{\circ}, x = 36 0^{\circ}

Solution steps

cos (2 x) - 2 sin (x) = 1, 0^{\circ} < x \leq 36 0^{\circ}

Subtract

1

from both sides

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

Rewrite using trig identities

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

Solve by substitution

sin (x) = - 1, sin (x) = 0

sin (x) = - 1, 0 < x \leq 36 0^{\circ} : x = 27 0^{\circ}

sin (x) = 0, 0 < x \leq 36 0^{\circ} : x = 18 0^{\circ}, x = 36 0^{\circ}

Combine all the solutions

x = 27 0^{\circ}, x = 18 0^{\circ}, x = 36 0^{\circ}

cos (aπ) - 1 = 0

3 tan (2 θ) - 3 = 0

cos (θ) = \frac{4 k - 1}{3}

5 sin (x) - 4 = 0

tan^{2} (θ) - 2 tan (θ) - 3 = 0

What is the general solution for cos(2x)-2sin(x)=1,0<x<= 360 ?
The general solution for cos(2x)-2sin(x)=1,0<x<= 360 is x=270,x=180,x=360