y=sin2x+4sinx+5. Then which of the following statements is correct? (D: Domain, R: Range)
A
D=R
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B
D:[2,10]
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C
D:[2,10]−{0}
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D
R:[2,10]
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Solution
The correct option is DR:[2,10] y=sin2x+4sinx+5 ⇒y=(sin2x+4sinx+4)+1=(sinx+2)2+1 We know domain of sinx is R ∴ domain of y is R Also we know that −1≤sinx≤1 Thus range of y is [2,10]