What is the general solution for cos(x)=sec(x) ?

The general solution for cos(x)=sec(x) is x=2pin,x=pi+2pin

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cos(x)=sec(x)

cos (x) = sec (x)

x = 2 πn, x = π + 2 πn

Solution steps

cos (x) = sec (x)

Subtract

sec (x)

from both sides

cos (x) - sec (x) = 0

Rewrite using trig identities

\frac{1}{sec ( x )} - sec (x) = 0

Solve by substitution

sec (x) = 1, sec (x) = - 1

sec (x) = 1 : x = 2 πn

sec (x) = - 1 : x = π + 2 πn

Combine all the solutions

x = 2 πn, x = π + 2 πn

cos^{2} (x) = 2

2 sin^{2} (x) = 3 cos (x)

5 cos (θ) + 3 = 3 cos (θ) + 5

6 sec^{2} (x) - 8 = 0

(2 sin (2 x) + 3) (- 3 + tan^{2} (3 x)) = 0

What is the general solution for cos(x)=sec(x) ?
The general solution for cos(x)=sec(x) is x=2pin,x=pi+2pin