What is the general solution for cos(x)tan(x)=sin(2x) ?

The general solution for cos(x)tan(x)=sin(2x) is x=2pin,x=pi+2pin,x= pi/3+2pin,x=(5pi)/3+2pin

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cos(x)tan(x)=sin(2x)

cos (x) tan (x) = sin (2 x)

x = 2 πn, x = π + 2 πn, x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

Solution steps

cos (x) tan (x) = sin (2 x)

Subtract

sin (2 x)

from both sides

cos (x) tan (x) - sin (2 x) = 0

Rewrite using trig identities

cos (x) tan (x) - 2 cos (x) sin (x) = 0

Factor

cos (x) tan (x) - 2 cos (x) sin (x) : cos (x) (tan (x) - 2 sin (x))

cos (x) (tan (x) - 2 sin (x)) = 0

Solving each part separately

cos (x) = 0 or tan (x) - 2 sin (x) = 0

cos (x) = 0 : x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

tan (x) - 2 sin (x) = 0 : x = 2 πn, x = π + 2 πn, x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

Combine all the solutions

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn, x = 2 πn, x = π + 2 πn, x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

Since the equation is undefined for:

\frac{π}{2} + 2 πn, \frac{3 π}{2} + 2 πn

x = 2 πn, x = π + 2 πn, x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

2 ∣ sin (4 θ) ∣ = 0

250 sin (7 5^{\circ}) = 393.19 sin (4 5^{\circ} - θ)

tan (θ) = \frac{6}{6.71}

x, sin (x) - 1 = 0

sin^{2} (θ) = 1 + cos (2 θ)

What is the general solution for cos(x)tan(x)=sin(2x) ?
The general solution for cos(x)tan(x)=sin(2x) is x=2pin,x=pi+2pin,x= pi/3+2pin,x=(5pi)/3+2pin