## Easiest Way to find Maximum and Minimum Value of Trigonometric Identities

In SSC CGL Exam , you will always find at least one question where you will be asked to find either the Maximum or Minimum value of trigonometric Identities. On the request of several students, we are providing the easiest way to solve those kind of questions. Examples are also given so that you can understand the method easily.

## Type -1

Example -  (1)Find the maximum and Minimum Value of 3 sin 2x + 4 cos 2x
Sol- Here the 4> 3 so
•  Maximum Value = 4
• Minimum Value = 3

Example - (2) Find the maximum and Minimum Value of 5 sin 2x + 3 cos 2x
Sol - Here 5>3
• Maximum Value = 5
• Minimum Value = 3

## Type -2

Example - (1) Find the Maximum and Minimum Value of 3 sin x + 4 cos y
Sol- If you find the question of this kind, apply the above formulae.
• Maximum Value =  9 + 16   =  25   = 5
• Minimum Value = -  9 + 16   = -  25   =  - 5

(2) Find the Maximum and Minimum Value of 3 sin x + 2 cos y
Sol- If you find the question of this kind, apply the above formulae.
• Maximum Value =  9 + 4    13
• Minimum Value = -  9 + 4   = -  13

## Type-3

In case of sec2x, cosec2x, cot2x and tan2x, we cannot find the maximum value because they can have infinity as their maximum value. So in question containing these trigonometric identities, you will be asked to find the minimum values only. The typical question forms are listed below:
Example- (1) Find the Minimum value of 3 sin 2x + 4 cosec 2x
sol - this equation is a typical example of our type-3 so apply the formula 2 ab   so,

• Minimum Value = 2 3 x  4= 2 12
Example (2) Find the Minimum value of 9 cos 2x + 2 sec 2x
sol - this equation is a typical example of our type-3 so apply the formula 2 ab   so,

• Minimum Value = 2 9 x  2= 2 18
Example (3) -Find the Minimum value of 8 tan 2x + 7 cot 2x
sol - this equation is a typical example of our type-3 so apply the formula 2 ab   so,

• Minimum Value = 2 8 x  7= 2 56

## Type-4

In this type, we will give you the explanation of question which are different from type-1, type-2 and type-3. If you find this kind of questions, you will have to convert these questions into type-1,2 or 3 by  using trigonometric formulas

Example - Find the Minimum Value of  Sec 2x +  cosec 2x
Sol - 1 + tan 2x +  cosec 2x    --------------------------------------------(Sec 2x = 1 + tan 2x)
= 1+ tan 2x + 1 +  cot 2x ------------------------------------------------(cosec 2x = 1 + cot 2x )
=2 + tan 2x +  cot 2x---------------------------------------------------apply type-3 formula
=2 + 2  1 x  1
= 2 + 2
=4

ALL THE BEST!!!