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

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

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

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

x = \frac{π}{2} + πn

Solution steps

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

Subtract

5 cos (2 x) + 5

from both sides

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

Factor

cos (2 x) sin (x) + sin (x) - 5 cos (2 x) - 5 : (cos (2 x) + 1) (sin (x) - 5)

(cos (2 x) + 1) (sin (x) - 5) = 0

Solving each part separately

cos (2 x) + 1 = 0 or sin (x) - 5 = 0

cos (2 x) + 1 = 0 : x = \frac{π}{2} + πn

sin (x) - 5 = 0 :

No Solution

Combine all the solutions

x = \frac{π}{2} + πn

3 cot (θ) = 3

sec (x) = 1, - 2 π \leq x \leq 2 π

tan (t) = \frac{4}{3}, sin (t)

cos (x) = \frac{2}{6}

16 sin^{2} (x) = 9

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