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TRINA DAS

· started a discussion

· 1 Months ago

How (Question:97909.0)

How does the 5th line of solution come?

Question:
If f(x) = 4(|Sin x |+|cosx|), then find the range of f(x).
Options:
A) (4, 4)
B) (0, 4\(\sqrt[]{2}\))
C) ⌊4,4\(\sqrt[]{2}\)⌋
D) ⌊0, \(\sqrt[]{2}\)⌋
Solution:

Ans: (c) Given f(x) = 4[|Sin x |+|cosx|]

sin2x ≤|Sin x |and cos2x ≤|cos x |

∴ sin2x + cos2x ≤ |Sin x |+|cos x |

i.e., 1 ≤ |Sin x |+|cos x | ⇒ |Sin x |+|cos x |≥ 1

also the maximum value of Sinx + Cosx is \(\sqrt[]{1+1}\) =\(\sqrt[]{2}\)

∴ |Sin x|+|cos x|≤  \(\sqrt[]{2}\)

∴ 1 ≤ |Sin x|+|cos x|≤  \(\sqrt[]{2}\)

⇒ 4 ≤ 4 [|Sin x |+|cosx|] ≤ 4\(\sqrt[]{2}\)

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