What is the general solution for -sqrt(2)tan(θ)-sec(θ)=0 ?

The general solution for -sqrt(2)tan(θ)-sec(θ)=0 is θ=(5pi)/4+2pin,θ=(7pi)/4+2pin

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-sqrt(2)tan(θ)-sec(θ)=0

- 2 tan (θ) - sec (θ) = 0

θ = \frac{5 π}{4} + 2 πn, θ = \frac{7 π}{4} + 2 πn

Solution steps

- 2 tan (θ) - sec (θ) = 0

Express with sin, cos

\frac{- 1 - sin ( θ ) 2}{cos ( θ )} = 0

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

- 1 - sin (θ) 2 = 0

Move

1

to the right side

- sin (θ) 2 = 1

Divide both sides by

- 2

sin (θ) = - \frac{2}{2}

General solutions for

sin (θ) = - \frac{2}{2}

θ = \frac{5 π}{4} + 2 πn, θ = \frac{7 π}{4} + 2 πn

4 cos (x) = - sin^{2} (x) + 1, 0 \leq x \leq 2 π

2 \cdot sin (x) = tan (x)

0 = arcsin (x)

cos (x) = 0.5149, 0 \leq x < 2 π

sin (θ) - 0.2 cos (θ) = 0.704

What is the general solution for -sqrt(2)tan(θ)-sec(θ)=0 ?
The general solution for -sqrt(2)tan(θ)-sec(θ)=0 is θ=(5pi)/4+2pin,θ=(7pi)/4+2pin