What is the general solution for cos(θ)cos(3θ)-sin(θ)sin(3θ)=0 ?

The general solution for cos(θ)cos(3θ)-sin(θ)sin(3θ)=0 is θ= pi/8+(pin)/2 ,θ=(3pi)/8+(pin)/2

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cos(θ)cos(3θ)-sin(θ)sin(3θ)=0

cos (θ) cos (3 θ) - sin (θ) sin (3 θ) = 0

θ = \frac{π}{8} + \frac{πn}{2}, θ = \frac{3 π}{8} + \frac{πn}{2}

Solution steps

cos (θ) cos (3 θ) - sin (θ) sin (3 θ) = 0

Rewrite using trig identities

cos (θ + 3 θ) = 0

General solutions for

cos (θ + 3 θ) = 0

θ + 3 θ = \frac{π}{2} + 2 πn, θ + 3 θ = \frac{3 π}{2} + 2 πn

Solve

θ + 3 θ = \frac{π}{2} + 2 πn : θ = \frac{π}{8} + \frac{πn}{2}

Solve

θ + 3 θ = \frac{3 π}{2} + 2 πn : θ = \frac{3 π}{8} + \frac{πn}{2}

θ = \frac{π}{8} + \frac{πn}{2}, θ = \frac{3 π}{8} + \frac{πn}{2}

1 - 2 sin (θ) = cos (2 θ), 0 \leq θ \leq 2 π

2 sin^{2} (θ) + 5 sin (θ) - 12 = 0

cos (2 θ) = \frac{3}{5}, 9 0^{\circ} \leq θ \leq 18 0^{\circ}

tan (θ) = \frac{1}{- 1}

sin^{2} (x) - 4 cos (x) - 4 = 0, 0 \leq x \leq 2 π

What is the general solution for cos(θ)cos(3θ)-sin(θ)sin(3θ)=0 ?
The general solution for cos(θ)cos(3θ)-sin(θ)sin(3θ)=0 is θ= pi/8+(pin)/2 ,θ=(3pi)/8+(pin)/2