What is the general solution for 5sec(x)-2=3cos(x) ?

The general solution for 5sec(x)-2=3cos(x) is x=2pin

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5sec(x)-2=3cos(x)

5 sec (x) - 2 = 3 cos (x)

x = 2 πn

Solution steps

5 sec (x) - 2 = 3 cos (x)

Subtract

3 cos (x)

from both sides

5 sec (x) - 2 - 3 cos (x) = 0

Rewrite using trig identities

- 2 - \frac{3}{sec ( x )} + 5 sec (x) = 0

Solve by substitution

sec (x) = 1, sec (x) = - \frac{3}{5}

sec (x) = 1 : x = 2 πn

sec (x) = - \frac{3}{5} :

No Solution

Combine all the solutions

x = 2 πn

(sin (x)) (cos (x)) (tan (x)) + cos (2 x) = 1

tan (x) = \frac{20}{30}

sin (x) = sin (2 7^{\circ})

cos (a) = \frac{12}{37}

120 sin (x - 12 0^{\circ}) = 120 sin (x - 24 0^{\circ})

What is the general solution for 5sec(x)-2=3cos(x) ?
The general solution for 5sec(x)-2=3cos(x) is x=2pin