What is the general solution for sin(2x)=10cos(x) ?

The general solution for sin(2x)=10cos(x) is x= pi/2+2pin,x=(3pi)/2+2pin

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sin(2x)=10cos(x)

sin (2 x) = 10 cos (x)

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

Solution steps

sin (2 x) = 10 cos (x)

Subtract

10 cos (x)

from both sides

sin (2 x) - 10 cos (x) = 0

Rewrite using trig identities

- 10 cos (x) + 2 cos (x) sin (x) = 0

Factor

- 10 cos (x) + 2 cos (x) sin (x) : 2 cos (x) (sin (x) - 5)

2 cos (x) (sin (x) - 5) = 0

Solving each part separately

cos (x) = 0 or sin (x) - 5 = 0

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

sin (x) - 5 = 0 :

No Solution

Combine all the solutions

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

- 2 cos (3 θ) = 1, 0 \leq θ \leq 2 π

cos (a) = 0.998482

3 - 4 sin (θ) = 4 - 6 sin (θ)

\frac{cos ( x )}{sin ( x )} = - 0.00172

x, r^{3} = sin (x)

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