What is the general solution for sec^2(x)+0.5tan(x)-1=0 ?

The general solution for sec^2(x)+0.5tan(x)-1=0 is x=pin,x=-0.46364…+pin

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sec^2(x)+0.5tan(x)-1=0

sec^{2} (x) + 0.5 tan (x) - 1 = 0

x = πn, x = - 0.46364 \dots + πn

Solution steps

sec^{2} (x) + 0.5 tan (x) - 1 = 0

Rewrite using trig identities

tan^{2} (x) + 0.5 tan (x) = 0

Solve by substitution

tan (x) = 0, tan (x) = - \frac{1}{2}

tan (x) = 0 : x = πn

tan (x) = - \frac{1}{2} : x = arctan (- \frac{1}{2}) + πn

Combine all the solutions

x = πn, x = arctan (- \frac{1}{2}) + πn

Show solutions in decimal form

x = πn, x = - 0.46364 \dots + πn

cos (2 x) = sin (x), 0 \leq x \leq 2 π

tan (x - \frac{π}{2}) = 1

5 cos (x) = 4 sin (x) + 4

6 sec^{2} (x) tan (x) = 8 tan (x)

csc (θ) = 0

What is the general solution for sec^2(x)+0.5tan(x)-1=0 ?
The general solution for sec^2(x)+0.5tan(x)-1=0 is x=pin,x=-0.46364…+pin