What is the general solution for 2sec^2(x)=5tan(x) ?

The general solution for 2sec^2(x)=5tan(x) is x=1.10714…+pin,x=0.46364…+pin

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2sec^2(x)=5tan(x)

2 sec^{2} (x) = 5 tan (x)

x = 1.10714 \dots + πn, x = 0.46364 \dots + πn

Solution steps

2 sec^{2} (x) = 5 tan (x)

Subtract

5 tan (x)

from both sides

2 sec^{2} (x) - 5 tan (x) = 0

Rewrite using trig identities

(1 + tan^{2} (x)) \cdot 2 - 5 tan (x) = 0

Solve by substitution

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

tan (x) = 2 : x = arctan (2) + πn

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

Combine all the solutions

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

Show solutions in decimal form

x = 1.10714 \dots + πn, x = 0.46364 \dots + πn

cos^{2} (2 x) - 3 sin^{2} (x) - 1 = 0

sin (- t) = \frac{3}{10}

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

c, e = r (sec (\frac{c}{2}) - 1)

arctan (\frac{x}{3}) + arctan (\frac{x}{2}) = arctan (x)

What is the general solution for 2sec^2(x)=5tan(x) ?
The general solution for 2sec^2(x)=5tan(x) is x=1.10714…+pin,x=0.46364…+pin