Option D is correct.
The best explanation for the following [tex]\tan \frac{5 \pi}{6}[/tex]≠ [tex]\tan \frac{5 \pi}{6}[/tex] is; The angles do not have the same reference angle or the same sign.
Explanation:
Why: [tex]\tan \frac{5 \pi}{6}[/tex]≠ [tex]\tan \frac{5 \pi}{6}[/tex]
*Every trigonometry function is positive in the first quadrant.
*In second quadrant only sin is positive and its inverse cosec. Rest all the function are negative.
*In third quadrant gives positive value only for tan and its inverse i.e cot
*In fourth quadrant gives positive value only for cos and its inverse sec.
The value of [tex]\tan \frac{5 \pi}{6}[/tex] = -0.57735026919
and the value of [tex]\tan \frac{5 \pi}{6}[/tex] = -1.73205080757.
therefore, the values of [tex]\tan \frac{5 \pi}{6}[/tex]≠ [tex]\tan \frac{5 \pi}{6}[/tex].
Also,
the angle [tex]\frac{5\pi}{6}[/tex] lies in the second quadrant and the angle [tex]\frac{5\pi}{3}[/tex] lies in the fourth quadrant.
Hence, the angles do not have the same reference angle or the same sign.
