Use Coupon: CART20 and get 20% off on all online Study Material

Total Price: Rs.

There are no items in this cart.
Continue Shopping
anurag singhal Grade:


8 years ago

Answers : (1)

askIITianexpert IITDelhi
8 Points

Every base in above expression is +ve & not equal to 1 so that part of the requirement is fulfilled.

For tan-1x to be defined x could take any real value.

For (tan-1x)-1 to be defined x could take any real value except where tan-1x=0 ;i.e. x ≠0.

For log2/pi(tan-1x)-1 to be defined (tan-1x)-1 >0 ;i.e. x>0.

For log2log2/pi(tan-1x)-1  to be defined  log2/pi(tan-1x)-1 >0;or,(tan-1x)-1 >1;or, tan-1x<1;or,x<tan(1 radian).

At last for log10log2log2/pi(tan-1x)-1 to be defined log2log2/pi(tan-1x)-1 >0;or, log2/pi(tan-1x)-1 >1

or, (tan-1x)-1 <2/pi                 ....[coz' (2/pi)<1]

or, tan-1x>pi/2 which couldn't be possible for any real x.    ---[-¶/2≤tan-1x¶/2;principal values.]

Hence the given expression is not defined for any x or it's domain is a null set.

This could be easily deducted by doing last step first & such kind of intution could be mastered by good practice.I just give these steps for the thoroughness.

8 years ago
Think You Can Provide A Better Answer ?
Answer & Earn Cool Goodies
  • Complete JEE Main/Advanced Course and Test Series
  • OFFERED PRICE: Rs. 15,900
  • View Details
Get extra Rs. 1,272 off
USE CODE: Neerajwin
Get extra Rs. 136 off
USE CODE: Neerajwin

Ask Experts

Have any Question? Ask Experts

Post Question

Answer ‘n’ Earn
Attractive Gift
To Win!!! Click Here for details