UPSEE Solved Model Paper 5

Let y = tan3xtanx
Then y =

3tanx−tan3x

(1−3tan2x)

×

1

tanx

⇒ y =

3−tan2x

1−3tan2x

⇒ tan2x(3y−1) = y - 3
⇒ tan2x =

y−3

3y−1

Since tan2x ≥ 0 for all x
∴

y−

3y−1

≥ 0
⇒ (y - 3) (3y - 1) ≥ 0
⇒ y <

1

3

or y ≥ 3
⇒ does not lie between

1

3

and 3