Question

If tan (3x + 30°) = 1 then find the value of x.

Answer 1

Hint : Here, compare the value of tangent given to the value of tangent of standard angle. Then equate their angle and simplify finding the value of x. Remember the value of tan 45 is 1.

Complete step-by-step answer :
Given,
tan (3x + 30°) = 1
We know tan 45° = 1
$\Rightarrow$ tan (3x + 30°) = tan 45°
On comparing angles
$\Rightarrow$ 45° = 3x + 30°
Rearranging the terms
$\Rightarrow$ 3x = 45° − 30°
$\Rightarrow$ 3x = 15°​
$\Rightarrow x = \dfrac{{15}}{3} = 5$
Thus, x = 5°
So, the correct answer is “x = 5°”.

Note : In these types of questions, you must use the value of tangent of standard angle. In trigonometry sine, cosine, tangent, cotangent, secant, cosecant are trigonometric tools, basically are ratios of different sides of a triangle, here they can be considered as ratios of right angle triangles. For acute angles we can find these ratios without knowing the actual side of that triangle. And can use those ratios for particular angles and can find the unknown side is one side and angle is known. Example: we know tan 45° = 1, and tangent is the ratio of perpendicular and base of angle 45°. From this, we can observe that if one angle of a right angle triangle is 45°, then base and its height is always equal.