What is the general solution for 3sec^2(x)-5tan(x)=3 ?

The general solution for 3sec^2(x)-5tan(x)=3 is x=1.03037…+pin,x=pin

Popular >

3sec^2(x)-5tan(x)=3

3 sec^{2} (x) - 5 tan (x) = 3

x = 1.03037 \dots + πn, x = πn

Solution steps

3 sec^{2} (x) - 5 tan (x) = 3

Subtract

3

from both sides

3 sec^{2} (x) - 5 tan (x) - 3 = 0

Rewrite using trig identities

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

Solve by substitution

tan (x) = \frac{5}{3}, tan (x) = 0

tan (x) = \frac{5}{3} : x = arctan (\frac{5}{3}) + πn

tan (x) = 0 : x = πn

Combine all the solutions

x = arctan (\frac{5}{3}) + πn, x = πn

Show solutions in decimal form

x = 1.03037 \dots + πn, x = πn

sin (2 x) cos (6 x) - cos (2 x) sin (6 x) = - 0.55

\frac{1}{cos ( x )} = - 1

3 tan^{3} (θ) - tan (θ) = 3 tan^{2} (θ) - 1

\frac{sin ( ( 2 \cdot 5 + 1 ) \cdot \frac{w}{2} )}{sin ( \frac{w}{2} )} = 0

sin (θ) = - 0.7

What is the general solution for 3sec^2(x)-5tan(x)=3 ?
The general solution for 3sec^2(x)-5tan(x)=3 is x=1.03037…+pin,x=pin