Question

Which of the following is greatest?

• A. $\tan 1$
• B. $\tan 4$
• C. $\tan 7$
• D. $\tan 10$

Answer 1

The correct option is A $\tan 1$

b. $\tan 4=\tan (\pi +(4-\pi ))=\tan (4-\pi )=\tan \left(0.86\right)$

c. $\tan 7=\tan (2\pi +(7-2\pi ))=\tan (7-2\pi )=\tan \left(0.72\right)$

d. $\tan 10=\tan (3\pi +(10-3\pi ))=\tan (10-3\pi )=\tan \left(0.58\right)$

Now $1>0.86>0.72>0.58$

$\Rightarrow$ $\tan 1>\tan \left(0.86\right)>\tan \left(0.72\right)>\tan \left(0.58\right)$

[as 1, 0.86, 0.72, 0.58 lies in the first quadrant and tangent function increase in all the quadrant]

Hence, $\tan 1$ is greatest