 ## Book: RD Sharma - Mathematics

### Chapter: 7. Values of Trigonometric Functions at Sum of Difference of Angles

#### Subject: Maths - Class 11th

##### Q. No. 1 of Exercise 7.2

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##### Find the maximum and minimum values of each of the following trigonometrical expressions:(i) 12 sin x- 5 cos x(ii) 12 cos x + 5 sin x+ 4(iii) (iv) sin x – cos x + 1

We know that the maximum value of Acosα + Bsinα + c is

c + √(A2 +B2)

And the minimum value is c - √(a2 +B2).

(i) Given f(x) = 12 sin x – 5 cos x

Here A = -5,B = 12 and c = 0   -13 12 sin x - 5 cos x ≤ 13

Hence, the maximum and minimum values of f(x) are 13 and -13 respectively.

(ii) Given f(x) = 12 cos x + 5 sin x + 4

Here A = 12,B = 5 and c = 4   -9 ≤ 12 cos x + 5 sin x + 4 ≤ 17

Hence, the maximum And minimum values of f(x) are 17 And -9 respectively.

(iii) Given We know that sin(A -B) = sinA cosB - cosA sinB   Here    -3 ≤ 11

Hence, the maximum And minimum values of f(x) are 11 And -3 respectively.

(iv) Given f(x) = sin x – cos x + 1

Here A = -1,B = 1 And c = 1   Hence, the maximum And minimum values of f(x) are And respectively.

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