What is the general solution for sin(x)-sqrt(3)cos(x)=1,0<= x<2pi ?

The general solution for sin(x)-sqrt(3)cos(x)=1,0<= x<2pi is x=(7pi)/6 ,x= pi/2

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sin(x)-sqrt(3)cos(x)=1,0<= x<2pi

sin (x) - 3 cos (x) = 1, 0 \leq x < 2 π

x = \frac{7 π}{6}, x = \frac{π}{2}

Solution steps

sin (x) - 3 cos (x) = 1, 0 \leq x < 2 π

Add

3 cos (x)

to both sides

sin (x) = 1 + 3 cos (x)

Square both sides

sin^{2} (x) = (1 + 3 cos (x))^{2}

Subtract

(1 + 3 cos (x))^{2}

from both sides

sin^{2} (x) - 1 - 23 cos (x) - 3 cos^{2} (x) = 0

Rewrite using trig identities

- 4 cos^{2} (x) - 2 cos (x) 3 = 0

Solve by substitution

cos (x) = - \frac{3}{2}, cos (x) = 0

cos (x) = - \frac{3}{2}, 0 \leq x < 2 π : x = \frac{5 π}{6}, x = \frac{7 π}{6}

cos (x) = 0, 0 \leq x < 2 π : x = \frac{π}{2}, x = \frac{3 π}{2}

Combine all the solutions

x = \frac{5 π}{6}, x = \frac{7 π}{6}, x = \frac{π}{2}, x = \frac{3 π}{2}

Verify solutions by plugging them into the original equation

x = \frac{7 π}{6}, x = \frac{π}{2}

sin (α) + 1 = cos (α)

\frac{sin ( 11 5 ^{\circ} )}{53} = \frac{sin ( S )}{83}

2 cos (x) - tan (x) = 0

0 = 3 sin (x)

sin (\frac{θ}{2}) = 0.4

What is the general solution for sin(x)-sqrt(3)cos(x)=1,0<= x<2pi ?
The general solution for sin(x)-sqrt(3)cos(x)=1,0<= x<2pi is x=(7pi)/6 ,x= pi/2