Question

please solve it as soon as possible​

Answer 1

Answer:

Let  y = 3 sin x + 4 cos x - 5.

⇒ (y+5) = 3 sin x + 4 cos x

Recall that for all real values of x,

−√(a2+b2) ≤ ( a sin x + b cos x ) ≤ √(a2+b2) → (1)

⇒ −√(32 + 42) ≤ (y+5) ≤ +√(32 + 42)    [From (1)]

⇒ −5 ≤ ( y + 5 ) ≤ 5

⇒ −5 − 5 ≤ [( y + 5 ) − 5] ≤ 5 − 5

⇒ −10 ≤ y ≤ 0

⇒ −10 ≤ (3 sin x + 4 cos x − 5) ≤ 0

Hence the range is [−10, 0].

As simple as that.... If you didn't get something do

Step-by-step explanation: