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

The general solution for sqrt(2)sec(x)-3tan(x)=-tan(x) is x= pi/4+2pin,x=(3pi)/4+2pin

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sqrt(2)sec(x)-3tan(x)=-tan(x)

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

x = \frac{π}{4} + 2 πn, x = \frac{3 π}{4} + 2 πn

Solution steps

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

Subtract

- tan (x)

from both sides

2 sec (x) - 2 tan (x) = 0

Express with sin, cos

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

\frac{f ( x )}{g ( x )} = 0 \Rightarrow f (x) = 0

2 - 2 sin (x) = 0

Move

2

to the right side

- 2 sin (x) = - 2

Divide both sides by

- 2

sin (x) = \frac{2}{2}

General solutions for

sin (x) = \frac{2}{2}

x = \frac{π}{4} + 2 πn, x = \frac{3 π}{4} + 2 πn

cot (θ) + csc (θ) = - 3

3 tan^{2} (θ) + 1 = \frac{2}{tan ^{2} ( θ )}

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

sin (x) + cos (x) + cot (x) = csc (x)

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

What is the general solution for sqrt(2)sec(x)-3tan(x)=-tan(x) ?
The general solution for sqrt(2)sec(x)-3tan(x)=-tan(x) is x= pi/4+2pin,x=(3pi)/4+2pin