Question

Lines `L_1` and `L_2` have slopes m and n, respectively, suppose `L_1` makes twice as large angle with the horizontal (mesured counter clockwise from the positive x-axis as does `L_2` and `L_1` has 4 times the slope of `L_2`. If `L_1` is not horizontal, then the value of the proudct mn equals.

Answer 1

Correct Answer - 2
Let `m=tan2theta` and `n=tantheta`
And `m=4n`
and `mne0`.
`therforetan 2theta ne 0`
`therefore thetane0`
`tan 2theta =4tan theta`
`rArr(2tantheta)/(1-tan^2theta)=4tantheta`
`rArr2 tan ^2theta =1`
`rArrtan^2theta=1//2`
`rArrmn=tan2theta.tantheta`
`=(2tan^2theta)/(1-tan^2theta)=(1)/(1-(//2))=2`