What is the general solution for cos(2θ)-sin(θ)cos(θ)=0 ?

The general solution for cos(2θ)-sin(θ)cos(θ)=0 is θ=(1.10714…)/2+(pin)/2

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cos(2θ)-sin(θ)cos(θ)=0

cos (2 θ) - sin (θ) cos (θ) = 0

θ = \frac{1.10714 \dots}{2} + \frac{πn}{2}

Solution steps

cos (2 θ) - sin (θ) cos (θ) = 0

Rewrite using trig identities

1 - \frac{tan ( 2 θ )}{2} = 0

Move

1

to the right side

- \frac{tan ( 2 θ )}{2} = - 1

Multiply both sides by

2

- tan (2 θ) = - 2

Divide both sides by

- 1

tan (2 θ) = 2

Apply trig inverse properties

2 θ = arctan (2) + πn

Solve

2 θ = arctan (2) + πn : θ = \frac{arctan ( 2 )}{2} + \frac{πn}{2}

θ = \frac{arctan ( 2 )}{2} + \frac{πn}{2}

Show solutions in decimal form

θ = \frac{1.10714 \dots}{2} + \frac{πn}{2}

\frac{cos ( x )}{2} - \frac{1}{2} = 0

tan (x) = \frac{4}{7}

sin (x) = - \frac{8}{9}

cos^{2} (θ) + 2 cos (θ) = 3

cos^{2} (x) = \frac{1}{9}

What is the general solution for cos(2θ)-sin(θ)cos(θ)=0 ?
The general solution for cos(2θ)-sin(θ)cos(θ)=0 is θ=(1.10714…)/2+(pin)/2