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

The general solution for sin(2x)+cos(x)=0,0<= x<= 2pi is x= pi/2 ,x=(3pi)/2 ,x=(7pi)/6 ,x=(11pi)/6

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sin(2x)+cos(x)=0,0<= x<= 2pi

sin (2 x) + cos (x) = 0, 0 \leq x \leq 2 π

x = \frac{π}{2}, x = \frac{3 π}{2}, x = \frac{7 π}{6}, x = \frac{11 π}{6}

Solution steps

sin (2 x) + cos (x) = 0, 0 \leq x \leq 2 π

Rewrite using trig identities

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

Factor

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

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

Solving each part separately

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

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

2 sin (x) + 1 = 0, 0 \leq x \leq 2 π : x = \frac{7 π}{6}, x = \frac{11 π}{6}

Combine all the solutions

x = \frac{π}{2}, x = \frac{3 π}{2}, x = \frac{7 π}{6}, x = \frac{11 π}{6}

cos (θ) = - 0.5

sec (x) = \frac{5}{3}

x, y = \frac{sec ( x )}{cos ^{1} ( x )} + 8 y^{2}

3 cot^{2} (θ) - 4 csc (θ) = 1

sin (2 x) sin (x) = 0

What is the general solution for sin(2x)+cos(x)=0,0<= x<= 2pi ?
The general solution for sin(2x)+cos(x)=0,0<= x<= 2pi is x= pi/2 ,x=(3pi)/2 ,x=(7pi)/6 ,x=(11pi)/6