Question

HELP ME PLZ!!! This is too hard

Answer 1

The solution of this trigonometric identity is
`\theta = 56.310^(\circ) \pm 180\cdot i ^(\circ)`,
`\forall \,i\in \mathbb{N}_(O)`.

Explanation:

Let
`7\cdot \tan \theta - 8 = 5\cdot \tan \theta -5`, we proceed to simplify the expression and solve afterwards either by algebraic or by trigonometric means:

`7\cdot \tan \theta -8 = 5\cdot \tan \theta -5`

`2\cdot \tan \theta = 3`

`\tan \theta = (3)/(2)`

`\theta = \tan^(-1) (3)/(2)`

The tangent is a trigonometric function with a period of 180°. Hence, we find that the family of angles associated with such value is:

`\theta = 56.310^(\circ) \pm 180\cdot i ^(\circ)`,
`\forall \,i\in \mathbb{N}_(O)`