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

The general solution for cos(x)-sin(3x)=0 is x=(pi+4pin)/8 ,x=(pi+4pin)/4

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

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

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

Solution steps

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

Add

sin (3 x)

to both sides

cos (x) = sin (3 x)

Rewrite using trig identities

cos (x) = sin (\frac{π}{2} - x)

Apply trig inverse properties

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

3 x = \frac{π}{2} - x + 2 πn : x = \frac{π + 4 πn}{8}

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

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

sin^{2} (x) = 20 - sin (x)

\frac{cos ( x )}{1 - cos ^{2} ( x )} = \frac{2}{3}

2 cos (x) - cos^{2} (x) = 0

- sec^{2} (x) - 5 = 2 sec (x) - 4

2 sin^{2} (x) + 2 sin (x) = 0

What is the general solution for cos(x)-sin(3x)=0 ?
The general solution for cos(x)-sin(3x)=0 is x=(pi+4pin)/8 ,x=(pi+4pin)/4