__Few points to remember:__- sinθ and cosθ both have "1" as their maximum value and "-1" as their minimum value. Hence the values of sinx, sin2x, cosx, cos3x, etc. lie between -1 and 1.
- For sin
^{2}x and cos^{2}x - Minimum value = 0
- Maximum value = 1
- For sinxcosx
- Minimum value = -1/2
- Maximum value = 1/2
- Minimum value of (sin θ cos θ)n = (-1/2)n

Some SSC CGL questions :

**Q. 1) What is the least value of 2sin**

^{2}θ + 3cos^{2}θ**(A) 1 (B) 2 (C) 3 (D) 0**

Since 2 is less than 3

Minimum value = 2

Minimum value = 2

**Answer: (B)**

**Hence the least value of 4sec**

^{2}θ + 9cosec

^{2}θ = 13 + 12 = 25

**Answer: (C)**

**Q. 4) The maximum of 3sinx - 4cosx is**

**(A) -1 (B) 5 (C) 7 (D) 9**

Maximum value = √(3^2 + 4^2) = √25 = 5

**Answer: (B)**

**Sometimes they ask the minimum/maximum value of a function. In CGL, that function would always be quadratic (ax**

^{2}+ bx + c). Please note that a quadratic function can't have both maximum and minimum values.**If "a" is positive, then the quadratic function will only have a minimum value. The maximum value would be infinite.****If****"a" is negative, then the quadratic function will only have a maximum value. The minimum value would be infinite.**

But the process to find both minimum and maximum values is same. Hence you shouldn't be worried about the words "maximum" or "minimum". When finding the minimum/maximum value of a function, we use the concept of "differentiation". Although differentiation is a wide topic in itself, but for CGL purpose, we only have to learn the basics.

**Just remember following things:**

- Differentiation of ax
^{n}= a*n*x^{n-1}. Hence differentiation of 4x^{3}= 12x^{2}and differentiation of 3x^{2}= 6x - Differentiation of ax = a. Hence differentiation of 4x is 4.
- Differentiation of any constant is zero. Hence differentiation of 5 is 0.
- If you have to differentiate ax
^{2}+ bx + c, just differentiate each of its term separately and add the result. __Process of finding the minimum value of a function__:- Differentiate the function
- What ever result you get, equate it with zero
- Find the value of x
- Put this value of x in the original function to get the minimum value.

**Let us solve a CGL question:**

**Q. 5) Find the minimum value of (x - 2)(x - 9)**

(A) -11/4 (B) 49/4 (C) 0 (D) -49/4

(A) -11/4 (B) 49/4 (C) 0 (D) -49/4

(x - 2)(x - 9) = x^2 - 11x + 18

Now we will differentiate (x^2 - 11x + 18)

Note that in this question, the value of a is positive, i.e., +1 and hence the question has asked you the "minimum" value. Had the value of "a" been negative (like -1), they would have asked you the "maximum" value.

Hence, differentiation of (x^2 - 11x + 18) = 2x - 11

Now 2x - 11 = 0

x = 11/2

Put x = 11/2 in (x^2 - 11x + 18) to get the minimum value

Minimum value of x^2 - 11x + 18 = (11/2)^2 - 11*(11/2) + 18 = -49/4

**Answer: (D)**

**If you have any doubt in this article, please drop a comment...**

Keep reading :)

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Another wonderful article.its fantabulous sir.Please post some reasoning hacks and general hacks for cgl like eliminating options,option substitution etc

ReplyDeleteThis topic of trigo was troubling me for quite sometime. This article explains everything with utmost clarity. Amazing work sir. Thank You so much.

ReplyDeleteSir please post hack for English too...

ReplyDeleteBcs this being a rank decided section of cgl

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ReplyDeleteu hv given explaination for finding min value of quadratic eqn. Plse provide us the method to find its max value too.

Thanx for ur genuine effort sir.

ReplyDeleteu hv given explaination for finding min value of quadratic eqn. Plse provide us the method to find its max value too.

The process to find the minimum and maximum values is same. I have added an explanation in the article. Please read the quadratic function part again.

DeleteSir ,

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No. You cant make any changes after exams or now.

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Hmmm...No coaching.

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