What is the general solution for sin(9x)-cos(x)=0 ?

The general solution for sin(9x)-cos(x)=0 is x=(pi+4pin)/(20),x=(pi+4pin)/(16)

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sin(9x)-cos(x)=0

sin (9 x) - cos (x) = 0

x = \frac{π + 4 πn}{20}, x = \frac{π + 4 πn}{16}

Solution steps

sin (9 x) - cos (x) = 0

Add

cos (x)

to both sides

sin (9 x) = cos (x)

Rewrite using trig identities

sin (9 x) = sin (\frac{π}{2} - x)

Apply trig inverse properties

9 x = \frac{π}{2} - x + 2 πn, 9 x = π - (\frac{π}{2} - x) + 2 πn

9 x = \frac{π}{2} - x + 2 πn : x = \frac{π + 4 πn}{20}

9 x = π - (\frac{π}{2} - x) + 2 πn : x = \frac{π + 4 πn}{16}

x = \frac{π + 4 πn}{20}, x = \frac{π + 4 πn}{16}

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

t, 0.08 = 0.1 cos (4 t)

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

ϕ, (x cos (ϕ))^{2} = x^{2} sin^{2} (ϕ) (1)

cos (18 0^{\circ} - x) = sin (- 30 0^{\circ})

What is the general solution for sin(9x)-cos(x)=0 ?
The general solution for sin(9x)-cos(x)=0 is x=(pi+4pin)/(20),x=(pi+4pin)/(16)