What is the general solution for 3sin(x)cos(x)+5cos(x)=0 ?

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

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3sin(x)cos(x)+5cos(x)=0

3 sin (x) cos (x) + 5 cos (x) = 0

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

Solution steps

3 sin (x) cos (x) + 5 cos (x) = 0

Factor

3 sin (x) cos (x) + 5 cos (x) : cos (x) (3 sin (x) + 5)

cos (x) (3 sin (x) + 5) = 0

Solving each part separately

cos (x) = 0 or 3 sin (x) + 5 = 0

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

3 sin (x) + 5 = 0 :

No Solution

Combine all the solutions

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

5 sin (x) tan (x) = - 7 tan (x)

cos (x + \frac{π}{2}) - cos (x - \frac{π}{2}) = 2

tan (2 x) + 1 = sec (2 x)

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

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

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