What is the general solution for sec(x/2)=cos(x/2) ?

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

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sec(x/2)=cos(x/2)

sec (\frac{x}{2}) = cos (\frac{x}{2})

x = 4 πn, x = 2 π + 4 πn

Solution steps

sec (\frac{x}{2}) = cos (\frac{x}{2})

Subtract

cos (\frac{x}{2})

from both sides

sec (\frac{x}{2}) - cos (\frac{x}{2}) = 0

Rewrite using trig identities

- \frac{1}{sec ( \frac{x}{2} )} + sec (\frac{x}{2}) = 0

Solve by substitution

sec (\frac{x}{2}) = 1, sec (\frac{x}{2}) = - 1

sec (\frac{x}{2}) = 1 : x = 4 πn

sec (\frac{x}{2}) = - 1 : x = 2 π + 4 πn

Combine all the solutions

x = 4 πn, x = 2 π + 4 πn

sec^{2} (x) - 2 tan^{2} (x) = 0

tan (5 x) + 3 = 0

2 tan (x) sin (x) - 7 sin (x) = 0

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

- 3 sin^{2} (θ) + 3 = - 10 cos (θ) - 3

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