What is the general solution for 5sec(x)-4cos(x)=8 ?

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

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5sec(x)-4cos(x)=8

5 sec (x) - 4 cos (x) = 8

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

Solution steps

5 sec (x) - 4 cos (x) = 8

Subtract

8

from both sides

5 sec (x) - 4 cos (x) - 8 = 0

Rewrite using trig identities

- 8 - \frac{4}{sec ( x )} + 5 sec (x) = 0

Solve by substitution

sec (x) = 2, sec (x) = - \frac{2}{5}

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

sec (x) = - \frac{2}{5} :

No Solution

Combine all the solutions

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

sin^{3} (x) = - 1

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

sin (x) + sin^{2} (x) + cos (x) + cos^{2} (x) = 0

4 cos^{2} (x) - 4 sin (x) - 1 = 0

cos^{2} (x) + 1 = - 2 cos (x)

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