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Sagot :
45° only the possible values for x.
What is the meaning of trigonometric ratio?
- Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle.
- The ratios of sides of a right-angled triangle with respect to any of its acute angles are known as the trigonometric ratios of that particular angle.
The given equation can be presented as follows;
[tex]\frac{cos (2 . x )}{cosine(x) + sin(x)} = 0[/tex]
We have that cos(2·x) = cos²(x) - sin²(x)
Also, we have, by the difference of two squares, the following relation;
cos²(x) - sin²(x) = (cos(x) - sin(x))(cos(x) + sin(x))
Therefore, the given equation can be written as follows;
[tex]\frac{cos (2 . x )}{cosine (x) + sin(x) } = \frac{(cos(x) - sin(x) * (cos(x) + sin(x)}{(cos(x) + sin(x))} = 0[/tex]
Crossing the common term, (cos(x) + sin(x)), in the numerator and the denominator, we have-
[tex]\frac{(cos(x) - sin (x) * (cos(x) + sin(x)}{(cos(x) + sin(x))} = cos (x) - sin(x) = 0[/tex]
From cos(x) - sin(x) = 0, we have;
Adding sin(x) to both sides of the equation
cos(x) - sin(x) + sin(x) = 0 + sin(x)
cos(x) = sin(x)
Therefore, the opposite leg and the adjacent leg of the right triangle formed with reference to the angle x are equal
∴ x = 90/2 = 45° only for 0° ≤ x ≤ 180°
Learn more about trigonometric ratio
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