What is the general solution for 4*cos(x)+3*sec(x)=8 ?

The general solution for 4*cos(x)+3*sec(x)=8 is x= pi/3+2pin,x=(5pi)/3+2pin

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4cos(x)+3sec(x)=8

4 \cdot cos (x) + 3 \cdot sec (x) = 8

x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

Solution steps

4 cos (x) + 3 sec (x) = 8

Subtract

8

from both sides

4 cos (x) + 3 sec (x) - 8 = 0

Rewrite using trig identities

- 8 + \frac{4}{sec ( x )} + 3 sec (x) = 0

Solve by substitution

sec (x) = 2, sec (x) = \frac{2}{3}

sec (x) = 2 : x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

sec (x) = \frac{2}{3} :

No Solution

Combine all the solutions

x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

\frac{3}{5} = sin (x)

\frac{sin ^{2} ( x )}{1 - cos ^{2} ( x )} = cot (x)

cos^{2} (x) + cos^{3} (x) + cos^{4} (x) + cos^{5} (x) = 0

sin^{2} (x) - 4 sin (x) = - 3

1 + 7 sinh (x) = 4 cosh^{2} (x)

What is the general solution for 4*cos(x)+3*sec(x)=8 ?
The general solution for 4*cos(x)+3*sec(x)=8 is x= pi/3+2pin,x=(5pi)/3+2pin