What is the general solution for 4-5cos(x)=4+3sin(x) ?

The general solution for 4-5cos(x)=4+3sin(x) is x=-1.03037…+pin

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4-5cos(x)=4+3sin(x)

4 - 5 cos (x) = 4 + 3 sin (x)

x = - 1.03037 \dots + πn

Solution steps

4 - 5 cos (x) = 4 + 3 sin (x)

Subtract

4 + 3 sin (x)

from both sides

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

Rewrite using trig identities

- 5 - 3 tan (x) = 0

Move

5

to the right side

- 3 tan (x) = 5

Divide both sides by

- 3

tan (x) = - \frac{5}{3}

Apply trig inverse properties

x = arctan (- \frac{5}{3}) + πn

Show solutions in decimal form

x = - 1.03037 \dots + πn

\frac{tan ( θ ) cos ( θ )}{csc ( θ )} = sin (θ)

sin (θ) = \frac{44}{12}

cos (A) = \frac{2 ^{2} + 2.2 4 ^{2} - 2.2 4 ^{2}}{2 ( 2 ) ( 2.24 )}

cos (θ) = - \frac{3}{5}, θ, 3

sin (3 x) = 0.5

What is the general solution for 4-5cos(x)=4+3sin(x) ?
The general solution for 4-5cos(x)=4+3sin(x) is x=-1.03037…+pin