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Range of f(x)=cos 2 x(cos 2 x+1)+2sin 2 x is... Please explain each step.

Range of f(x)=cos2x(cos2x+1)+2sin2x is...
Please explain each step.

Grade:12

1 Answers

Vikas TU
14149 Points
5 years ago
Write cos2x(cos2x+1)+2sin2x as:
(cos^4x+cos^2x)+2sin2x
Now,
(cos^4x+cos^2x)+2 – 2cos^2x
=> cos^4x – cos^2x + 2
=>cos^4x + 1 + sin^2x
Range = > [2,2]

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