skeeter said:another approach ...
$\tan{\alpha} = \cot{\beta}$
$\dfrac{\sin{\alpha}}{\cos{\alpha}} = \dfrac{\cos{\beta}}{\sin{\beta}}$
$\cos{\alpha} \cdot \cos{\beta} = \sin{\alpha} \cdot \sin{\beta}$
$\cos{\alpha} \cdot \cos{\beta} - \sin{\alpha} \cdot \sin{\beta} = 0$
$\cos(\alpha + \beta) = 0$
Monoxdifly said:I like this other approach since I can comprehend it easier. I got \(\displaystyle 30^{\circ}\) this way. Is that right?
skeeter said:substitute your solution into the original equation ...
is $\tan(55^\circ) = \cot(35^\circ)$ ?
A trigonometric equation is an equation that involves trigonometric functions such as sine, cosine, and tangent. These equations are used to solve problems related to angles and triangles.
To solve a trigonometric equation, you need to use algebraic techniques to isolate the trigonometric function and then use trigonometric identities to simplify the equation. You can also use a calculator to find the solutions.
The most common trigonometric identities used in solving equations are the Pythagorean identities, sum and difference identities, and double angle identities.
You can check your solution by substituting it back into the original equation and simplifying. If the resulting equation is true, then your solution is correct.
Trigonometric equations are used in many fields such as physics, engineering, and astronomy to solve real-world problems involving angles and distances. They are also used in navigation, surveying, and construction to determine the measurements of triangles and other geometric shapes.