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

The general solution for 4cos(x)+3cos(x)=5 is x=0.77519…+2pin,x=2pi-0.77519…+2pin

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

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

x = 0.77519 \dots + 2 πn, x = 2 π - 0.77519 \dots + 2 πn

Solution steps

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

Simplify

4 cos (x) + 3 cos (x) : 7 cos (x)

7 cos (x) = 5

Divide both sides by

7

cos (x) = \frac{5}{7}

Apply trig inverse properties

x = arccos (\frac{5}{7}) + 2 πn, x = 2 π - arccos (\frac{5}{7}) + 2 πn

Show solutions in decimal form

x = 0.77519 \dots + 2 πn, x = 2 π - 0.77519 \dots + 2 πn

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

3 sin (x) = 3 \cdot sin (x) + 3 cos (x) + 3 sin (x)

csc (θ) + 1 = 0, (0, 2 π)

x, y^{2} = - 2 tan (2 x)

2 cos^{2} (a) - 3 cos (a) + 1 = 0

What is the general solution for 4cos(x)+3cos(x)=5 ?
The general solution for 4cos(x)+3cos(x)=5 is x=0.77519…+2pin,x=2pi-0.77519…+2pin