Which of the following is the greatest? tan 1, tan 4, tan 7, tan 10

Options

A. tan 1
B. tan 4
C. tan 7
D. tan 10

Answer

tan 1

Explanation

`tan4=tan(pi+(4-pi))=tan(4-pi)=tan(0.86)`
`tan7=tan(2pi+(7-2pi))=tan(7-2pi)=tan(0.72)`
`tan10=ta(3pi+(10-3pi))=tan(10-3pi)=tan(0.58)`
Now, `1gt0.86gt0.72gt0.58`
`rArrtan1gttan(0.86)gttan(0.72)gttan(0.58)`
[as angles 1,0.86,0.72, 0.58 lie in the first quadrant and tangent function increases in all the quadrant]
Hence, among the given values, tan1 is the greatest.