Answer:
The solution of this trigonometric identity is [tex]\theta = 56.310^{\circ} \pm 180\cdot i ^{\circ}[/tex], [tex]\forall \,i\in \mathbb{N}_{O}[/tex].
Step-by-step explanation:
Let [tex]7\cdot \tan \theta - 8 = 5\cdot \tan \theta -5[/tex], we proceed to simplify the expression and solve afterwards either by algebraic or by trigonometric means:
[tex]7\cdot \tan \theta -8 = 5\cdot \tan \theta -5[/tex]
[tex]2\cdot \tan \theta = 3[/tex]
[tex]\tan \theta = \frac{3}{2}[/tex]
[tex]\theta = \tan^{-1} \frac{3}{2}[/tex]
The tangent is a trigonometric function with a period of 180°. Hence, we find that the family of angles associated with such value is:
[tex]\theta = 56.310^{\circ} \pm 180\cdot i ^{\circ}[/tex], [tex]\forall \,i\in \mathbb{N}_{O}[/tex]
