# Tricks to find Max and Min Value of Trigonometric identity

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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)

(2)

(3)

(4)

(5)

(6)

QUESTIONS

(1)The greatest value of  is

(a)1

(b)1/2

(c) 0

(d)

Ans.(a)

(2)What is the minimum value of

(a)  0

(b)3/4

(c)   2

(d) 1/4

Ans.  (b)

(3)Find the maximum value of

(a)

(b)  1

(c)

(d)

Ans.  (d)      The maximum value of

The maximum value of

(4)Find the minimum value of

(a) 81

(b)41

(c)82

(d)90

Ans.   (a)

minimum value of

(5)  is maximum when is:

(a)150

(b)300

(c)450

(d)  600

Ans. (a)

The maximum value occurs when

(6)What is the maximum value of

(a)1/2

(b)1/4

(c)   1

(d)  None of these

Ans. (b)

(7)The greatest value of  is

(a)35

(b)34

(c)3

(d)33

Ans.(a)

For maximum value

maximum and maximum value is