What is the general solution for 2cos(α)=3tan(α) ?

The general solution for 2cos(α)=3tan(α) is α= pi/6+2pin,α=(5pi)/6+2pin

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2cos(α)=3tan(α)

2 cos (α) = 3 tan (α)

α = \frac{π}{6} + 2 πn, α = \frac{5 π}{6} + 2 πn

Solution steps

2 cos (α) = 3 tan (α)

Subtract

3 tan (α)

from both sides

2 cos (α) - 3 tan (α) = 0

Express with sin, cos

\frac{2 cos ^{2} ( α ) - 3 sin ( α )}{cos ( α )} = 0

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

2 cos^{2} (α) - 3 sin (α) = 0

Rewrite using trig identities

(1 - sin^{2} (α)) \cdot 2 - 3 sin (α) = 0

Solve by substitution

sin (α) = - 2, sin (α) = \frac{1}{2}

sin (α) = - 2 :

No Solution

sin (α) = \frac{1}{2} : α = \frac{π}{6} + 2 πn, α = \frac{5 π}{6} + 2 πn

Combine all the solutions

α = \frac{π}{6} + 2 πn, α = \frac{5 π}{6} + 2 πn

3 tan^{2} (θ) + 7 tan (θ) - 2 = - 4

8 sin (2 x) + 1 = 6

\frac{( 1 - cos ( x ) ) ( csc ^{2} ( x ) - 4 )}{1 + cos ( x )} = 0

6 sin (a) + 4 = 2 sin (a) + 8

sin (3 x) = 0, - 2 < x < 2

What is the general solution for 2cos(α)=3tan(α) ?
The general solution for 2cos(α)=3tan(α) is α= pi/6+2pin,α=(5pi)/6+2pin