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

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

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sin(2θ)+cos(θ)=0,0<= θ<= 2pi

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

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

Solution steps

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

Rewrite using trig identities

cos (θ) + 2 cos (θ) sin (θ) = 0

Factor

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

cos (θ) (2 sin (θ) + 1) = 0

Solving each part separately

cos (θ) = 0 or 2 sin (θ) + 1 = 0

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

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

Combine all the solutions

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

sin (1 0^{\circ}) = 2 sin (a) cos (a)

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

cos^{2} (x) = \frac{3}{5}

1 - sec^{2} (x) = tan^{2} (x)

csc^{2} (x) = (\frac{1}{cos ( x )})^{2}

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