Question:

The set of values of $ x $ for which $ \frac{tan 3x - tan 2x}{1+ tan 3x\,tan2x} = 1 $ is

Updated On: Aug 15, 2022
  • $ \phi $
  • { $ \frac{\pi}{4} $ }
  • { $ n\pi + \frac {\pi}{4} , n = 1,2, 3,... $ }
  • { $ 2n\pi + \frac {\pi}{4} , n = 1,2, 3,... $ }
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The Correct Option is A

Solution and Explanation

Answer (a) $ \phi $
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Concepts Used:

Sets

Set is the collection of well defined objects. Sets are represented by capital letters, eg. A={}. Sets are composed of elements which could be numbers, letters, shapes, etc.

Example of set: Set of vowels A={a,e,i,o,u}

Representation of Sets

There are three basic notation or representation of sets are as follows:

Statement Form: The statement representation describes a statement to show what are the elements of a set.

  • For example, Set A is the list of the first five odd numbers.

Roster Form: The form in which elements are listed in set. Elements in the set is seperatrd by comma and enclosed within the curly braces.

  • For example represent the set of vowels in roster form.

A={a,e,i,o,u}

Set Builder Form: 

  1. The set builder representation has a certain rule or a statement that specifically describes the common feature of all the elements of a set.
  2. The set builder form uses a vertical bar in its representation, with a text describing the character of the elements of the set.
  3. For example, A = { k | k is an even number, k ≤ 20}. The statement says, all the elements of set A are even numbers that are less than or equal to 20.
  4. Sometimes a ":" is used in the place of the "|".