What is the general solution for cos(x/3)=sin(x) ?

The general solution for cos(x/3)=sin(x) is x=(3pi+12pin)/8 ,x=(3pi+12pin)/4

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cos(x/3)=sin(x)

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

x = \frac{3 π + 12 πn}{8}, x = \frac{3 π + 12 πn}{4}

Solution steps

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

Rewrite using trig identities

cos (\frac{x}{3}) = sin (\frac{π}{2} - \frac{x}{3})

Apply trig inverse properties

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

x = \frac{π}{2} - \frac{x}{3} + 2 πn : x = \frac{3 π + 12 πn}{8}

x = π - (\frac{π}{2} - \frac{x}{3}) + 2 πn : x = \frac{3 π + 12 πn}{4}

x = \frac{3 π + 12 πn}{8}, x = \frac{3 π + 12 πn}{4}

1 + 4 \cdot sin (x) = 2

cos (θ) = \frac{7}{8}

sec (x) (2 sin (x) + 1) - 2 (2 sin (x) + 1) = 0

3 sin^{2} (x) + 2 cos (2 x) = 1

1 = sin (x) + 3 cos (x)

What is the general solution for cos(x/3)=sin(x) ?
The general solution for cos(x/3)=sin(x) is x=(3pi+12pin)/8 ,x=(3pi+12pin)/4