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

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

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3-3cos(θ)= 3/2 sec(θ)

3 - 3 cos (θ) = \frac{3}{2} sec (θ)

No Solution for θ \in R

Solution steps

3 - 3 cos (θ) = \frac{3}{2} sec (θ)

Subtract

\frac{3}{2} sec (θ)

from both sides

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

Simplify

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

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

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

6 - 6 cos (θ) - 3 sec (θ) = 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

18 sec^{2} (x) - 3 tan (x) = 21

sin^{2} (θ) - 2 cos (θ) = 2

3 + 4 sin (θ) = 0

tan (2 A) = \frac{( 2 tan ( A ) )}{[ 1 + ( tan ( A ) ) ^{2} ]}

cos (4 x) + 1 = 3 sin (2 x)

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