What is the general solution for tan^2(x)=sec(x) ?

The general solution for tan^2(x)=sec(x) is x=0.90455…+2pin,x=2pi-0.90455…+2pin

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tan^2(x)=sec(x)

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

x = 0.90455 \dots + 2 πn, x = 2 π - 0.90455 \dots + 2 πn

Solution steps

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

Subtract

sec (x)

from both sides

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

Rewrite using trig identities

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

Solve by substitution

sec (x) = \frac{1 + 5}{2}, sec (x) = \frac{1 - 5}{2}

sec (x) = \frac{1 + 5}{2} : x = arcsec (\frac{1 + 5}{2}) + 2 πn, x = 2 π - arcsec (\frac{1 + 5}{2}) + 2 πn

sec (x) = \frac{1 - 5}{2} :

No Solution

Combine all the solutions

x = arcsec (\frac{1 + 5}{2}) + 2 πn, x = 2 π - arcsec (\frac{1 + 5}{2}) + 2 πn

Show solutions in decimal form

x = 0.90455 \dots + 2 πn, x = 2 π - 0.90455 \dots + 2 πn

x, sin (x) - sin (2 x) = 0

sin (θ) = \frac{4}{5}, cos (θ)

sin (6 x) = cos (3 x)

sin (\frac{θ}{2}) - cos (\frac{θ}{2}) = 0

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

What is the general solution for tan^2(x)=sec(x) ?
The general solution for tan^2(x)=sec(x) is x=0.90455…+2pin,x=2pi-0.90455…+2pin