Tricks to find Max and Min Value of Trigonometric identity

Tricks to find Max and Min Value of Trigonometric identity

Dear Readers,

We are providing you trigonometric identity shortcuts which are usually asked in SSC Exams. Use these below short cuts to solve questions within minimum time. These shortcuts will be so  helpful for your upcoming SSC CGL Exam 2016.

Type-I

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 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:-2

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 -II

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

Example-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 III

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-IV

 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

This topic creates a lot of problem for students during exam time.

Limit of the values of Trigonometric Functions :

(1)image001

(2)image002

(3)image003

(4)image004

(5)image005

(6)image006

image007

QUESTIONS

(1)The greatest value of image008 is

(a)1

(b)1/2

(c) 0

(d) image010

Ans.(a)

Untitled

(2)What is the minimum value ofimage012

(a)  0

(b)3/4

(c)   2

(d) 1/4

Ans.  (b)

image015

(3)Find the maximum value of image016

(a) image017

(b)  1

(c) image018

(d)image019

Ans.  (d)      The maximum value of image020

 The maximum value of image021

(4)Find the minimum value of image022

(a) 81

(b)41

(c)82

(d)90

Ans.   (a)

minimum value of

image023

(5) image024 is maximum when image025is:

(a)150

(b)300

(c)450

(d)  600

Ans. (a)

5

The maximum value occurs when

image027

(6)What is the maximum value ofimage028

(a)1/2

(b)1/4

(c)   1

(d)  None of these

Ans. (b)

image029

image030

image031

(7)The greatest value of image032 is

(a)35

(b)34

(c)3

(d)33

Ans.(a)

image033

For maximum value

image034 maximum and maximum value is

image035

image036

 

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