What is the general solution for sin(2x)=5cos(x) ?

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

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sin(2x)=5cos(x)

sin (2 x) = 5 cos (x)

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

Solution steps

sin (2 x) = 5 cos (x)

Subtract

5 cos (x)

from both sides

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

Rewrite using trig identities

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

Factor

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

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

Solving each part separately

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

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

2 sin (x) - 5 = 0 :

No Solution

Combine all the solutions

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

sin (a) = 0.4848

sin^{2} (x) = 2 cos^{4} (x)

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

i, x sin^{2} (x) = cos^{2} (x)

c, sin^{2} (x) + 12 = 12 (sin (x) - cos (x))

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