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Question

3sinx + 4cosx + r is always greater than or equal to 0. What is the smallest value ‘r’ can to take

CAT 2021

A
5
CORRECT ANSWER WRONG ANSWER
B
-5
CORRECT ANSWER WRONG ANSWER
C
4
CORRECT ANSWER WRONG ANSWER
D
3
CORRECT ANSWER WRONG ANSWER
Solution

Correct option is

(A)

Explanatory Answer :

3sinx + 4cosx ≥ -r

5(3/5sinx + 4/5cosx) ≥ -r

3/5 = cosA => sinA =4/5

5(sinx cosA + sinA cosx) ≥ -r

5(sin(x + A)) ≥ -r

5sin (x + A) ≥ -r

-1 ≤ sin (angle) ≤ 1

5sin (x + A) ≥ -5

r(min) = 5

hence A is the correct option