What is the general solution for 3/2 sec(θ)+3cos(θ)=3 ?

The general solution for 3/2 sec(θ)+3cos(θ)=3 is No Solution for θ\in\mathbb{R}

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3/2 sec(θ)+3cos(θ)=3

\frac{3}{2} sec (θ) + 3 cos (θ) = 3

No Solution for θ \in R

Solution steps

\frac{3}{2} sec (θ) + 3 cos (θ) = 3

Subtract

3

from both sides

\frac{3}{2} sec (θ) + 3 cos (θ) - 3 = 0

Simplify

\frac{3}{2} sec (θ) + 3 cos (θ) - 3 : \frac{3 sec ( θ ) + 6 cos ( θ ) - 6}{2}

\frac{3 sec ( θ ) + 6 cos ( θ ) - 6}{2} = 0

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

3 sec (θ) + 6 cos (θ) - 6 = 0

Rewrite using trig identities

- 6 + \frac{6}{sec ( θ )} + 3 sec (θ) = 0

Solve by substitution

sec (θ) = 1 + i, sec (θ) = 1 - i

sec (θ) = 1 + i :

No Solution

sec (θ) = 1 - i :

No Solution

Combine all the solutions

No Solution for θ \in R

2 sec (x) cos^{2} (x) = csc^{2} (x) - cot^{2} (x)

1 = 7 cos (\frac{π}{3} t)

12 cos^{2} (x) + 2 cos (x) - 2 = 0

sin (θ) = - 0.94

sin (θ) = 0, 0 \leq θ \leq 2 π

What is the general solution for 3/2 sec(θ)+3cos(θ)=3 ?
The general solution for 3/2 sec(θ)+3cos(θ)=3 is No Solution for θ\in\mathbb{R}