Question

`lim_(thetato0)(1-cos4theta)/(1-cos6theta)` is equal to
A. `4/9`
B. `1/2`
C. `-1/2`
D. `-1`

Answer 1

Correct Answer - a
Given, `lim_(thetato0)(1-cos4theta)/(1-cos6theta) = lim_(thetato0)(2sin^(2)theta)/(2sin^(2)3theta)` `[therefore 1-cos2theta=2sin^(2)theta]`
`=(lim_(thetato0)(sin^(2)2theta)/(2theta)^(2).(2theta)^(2))/(lim_(thetato0)(sin^(2)3theta)/(3theta)^(2).(3theta)^(2))` =`4/9.(lim_(thetato0)((sin2theta)/(2theta))^(2))/(lim_(thetato0)((sin3theta)/(3theta))^(2))` `[therefore lim(xto0)(sinx)/(x) "and" xto0 rArr kx to0]`=`4/9`