Question

Let `tanx-tan^2x >0` and `|2s inx|<1` . Then the intersection of which of the following two sets satisfies both the inequalities? `x > npi,n in Z` (b) `x > npi-pi/6,n in Z` `xA. `x gt npi, n in Z`
B. `x gt npi-pi//6, n in Z`
C. `x lt n pi-pi//4, n in Z`
D. `x lt npi+pi//6, n in Z`

Answer 1

Correct Answer - A::D
`tan x-tan^(2) x gt 0`
or `tan x(tan x-1) lt 0`
or `0 lt tan x lt 1`
or `0 lt x lt pi//4`
`rArr n pi lt x lt n pi+pi//4, n in Z` (generalizing)
`|sin x| lt 1/2 rArr -1/2 lt sin x lt 1/2`
`rArr -pi//6 lt x lt pi//6`
`rArr -pi//6+n pi lt x lt pi/66+n pi, n in Z` (generalizing)
Then the common values are `npi lt x lt npi+pi//6`.