What is the general solution for cos(5θ)=sin(3θ) ?

The general solution for cos(5θ)=sin(3θ) is θ=(pi+4pin}{16},θ=-\frac{pi+4pin)/4

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cos(5θ)=sin(3θ)

cos (5 θ) = sin (3 θ)

θ = \frac{π + 4 πn}{16}, θ = - \frac{π + 4 πn}{4}

Solution steps

cos (5 θ) = sin (3 θ)

Rewrite using trig identities

cos (5 θ) = sin (\frac{π}{2} - 5 θ)

Apply trig inverse properties

3 θ = \frac{π}{2} - 5 θ + 2 πn, 3 θ = π - (\frac{π}{2} - 5 θ) + 2 πn

3 θ = \frac{π}{2} - 5 θ + 2 πn : θ = \frac{π + 4 πn}{16}

3 θ = π - (\frac{π}{2} - 5 θ) + 2 πn : θ = - \frac{π + 4 πn}{4}

θ = \frac{π + 4 πn}{16}, θ = - \frac{π + 4 πn}{4}

(2 sin (2 x) + 2 cos (2 x))^{2} = 4

sin (x) = \frac{7}{3}

0 = sin (4 x)

x, sin (x) = sin (2 x)

- 7 tan (A) - 14 = tan (A) - 6

What is the general solution for cos(5θ)=sin(3θ) ?
The general solution for cos(5θ)=sin(3θ) is θ=(pi+4pin}{16},θ=-\frac{pi+4pin)/4