What is the general solution for sin(x)*cos(x)-3cos(x)=0 ?

The general solution for sin(x)*cos(x)-3cos(x)=0 is x= pi/2+2pin,x=(3pi)/2+2pin

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sin(x)*cos(x)-3cos(x)=0

sin (x) \cdot cos (x) - 3 cos (x) = 0

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

Solution steps

sin (x) cos (x) - 3 cos (x) = 0

Factor

sin (x) cos (x) - 3 cos (x) : cos (x) (sin (x) - 3)

cos (x) (sin (x) - 3) = 0

Solving each part separately

cos (x) = 0 or sin (x) - 3 = 0

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

sin (x) - 3 = 0 :

No Solution

Combine all the solutions

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

9.8 \cdot sin (α) - 0.2 \cdot 9.8 \cdot cos (α) = 0.47

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

tan^{2} (θ) = \frac{sin ^{2} ( θ )}{cos ( θ )}

tan (x) = 1, 17

θ, 2 cot (θ) - 1 = 0

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