What is the general solution for sin(x)cos(x)=-9cos(x) ?

The general solution for sin(x)cos(x)=-9cos(x) is x= pi/2+2pin,x=(3pi)/2+2pin

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sin(x)cos(x)=-9cos(x)

sin (x) cos (x) = - 9 cos (x)

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

Solution steps

sin (x) cos (x) = - 9 cos (x)

Subtract

- 9 cos (x)

from both sides

sin (x) cos (x) + 9 cos (x) = 0

Factor

sin (x) cos (x) + 9 cos (x) : cos (x) (sin (x) + 9)

cos (x) (sin (x) + 9) = 0

Solving each part separately

cos (x) = 0 or sin (x) + 9 = 0

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

sin (x) + 9 = 0 :

No Solution

Combine all the solutions

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

5 tan (θ) - 7 = 0

cot^{2} (x) + 1 = sin^{2} (x)

(4 + tan (x)) (3 sin (x) - 2) = 0

sec (2 x) - 1 = 0

sin (2 x) + sin (x) + 2 cos (x) + 1 = 0

What is the general solution for sin(x)cos(x)=-9cos(x) ?
The general solution for sin(x)cos(x)=-9cos(x) is x= pi/2+2pin,x=(3pi)/2+2pin