Find Range of the function

Question

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Answer 1

-1 < cosx < 1

0 < (cosx)² < 1

0 < 2(cosx)² < 2

0 < 1+cos2x  < 2

-3 < 1+cos2x -3  < -1

-3 < cos2x -2  < -1

-3/2 < (cos2x -2)/2  < -1/2

9/4 < [(cos2x -2)/2]²  < 1/4

-7/2 + 9/4 <{ -7/2 +[(cos2x -2)/2]² } < -7/2 + 1/4

-5/4 < { -7/2 +[(cos2x -2)/2]² } < -13/4

-5/4 < { -7/2 +2 [(cosx)² -3/2]² } < -13/4