What is the general solution for cos(x/3)-cos(x/(15))=0 ?

The general solution for cos(x/3)-cos(x/(15))=0 is x=15pin,x=(15pi)/2+15pin,x=10pin,x=5pi+10pin

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cos(x/3)-cos(x/(15))=0

cos (\frac{x}{3}) - cos (\frac{x}{15}) = 0

x = 15 πn, x = \frac{15 π}{2} + 15 πn, x = 10 πn, x = 5 π + 10 πn

Solution steps

cos (\frac{x}{3}) - cos (\frac{x}{15}) = 0

Rewrite using trig identities

- 2 sin (\frac{2 x}{15}) sin (\frac{x}{5}) = 0

Solving each part separately

sin (\frac{2 x}{15}) = 0 or sin (\frac{x}{5}) = 0

sin (\frac{2 x}{15}) = 0 : x = 15 πn, x = \frac{15 π}{2} + 15 πn

sin (\frac{x}{5}) = 0 : x = 10 πn, x = 5 π + 10 πn

Combine all the solutions

x = 15 πn, x = \frac{15 π}{2} + 15 πn, x = 10 πn, x = 5 π + 10 πn

(2 cos (x) - 3) (2 sin (x) + 1) = 0

y, x = π - arcsin (y)

arctan (x) = 3

tan (x) cos (x) = cos (x)

4 cos^{2} (θ) - 2 = - 1

What is the general solution for cos(x/3)-cos(x/(15))=0 ?
The general solution for cos(x/3)-cos(x/(15))=0 is x=15pin,x=(15pi)/2+15pin,x=10pin,x=5pi+10pin