10.) Prove that tan 210- tan 150/= tan 60 1+tan 210 tan 150
Answers
Answer:
The value of tan 210 degrees is 0.5773502. . .. Tan 210 degrees in radians is written as tan (210° × π/180°), i.e., tan (7π/6) or tan (3.665191. . .). In this article, we will discuss the methods to find the value of tan 210 degrees with examples.
Tan 210°: 1/√3
Tan 210° in decimal: 0.5773502. . .
Tan (-210 degrees): -0.5773502. . . or -1/√3
Tan 210° in radians: tan (7π/6) or tan (3.6651914 . . .)
What is the Value of Tan 210 Degrees?
The value of tan 210 degrees in decimal is 0.577350269. . .. Tan 210 degrees can also be expressed using the equivalent of the given angle (210 degrees) in radians (3.66519 . . .)
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 210 degrees = 210° × (π/180°) rad = 7π/6 or 3.6651 . . .
∴ tan 210° = tan(3.6651) = 1/√3 or 0.5773502. . .
Tan 210 Degrees
Explanation:
For tan 210 degrees, the angle 210° lies between 180° and 270° (Third Quadrant). Since tangent function is positive in the third quadrant, thus tan 210° value = 1/√3 or 0.5773502. . .
Since the tangent function is a periodic function, we can represent tan 210° as, tan 210 degrees = tan(210° + n × 180°), n ∈ Z.
⇒ tan 210° = tan 390° = tan 570°, and so