How can I prove that this function is bounded using the given hint? f ( x ) = 1 − 2 sin ⁡ x 1 + cos 2 ⁡ x ,Hint:1. | A + B | ≤ | A | + | B | ,2. | sin ⁡ x | ≤ 1.

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How can I prove that this function is bounded using the given hint?  f  (  x  )  =            1      −      2      sin      ⁡      x              1      +              cos        2            ⁡      x        ,Hint:1.       |    A  +  B      |    ≤      |    A      |    +      |    B      |    ,2.       |    sin  ⁡  x      |    ≤  1.

Rachael Conner · Accepted Answer

1      −      2      sin      ⁡              x                    1      +              cos        2            ⁡      x        ≤                    |            1      −      2      sin      ⁡              x                    |                    1      +              cos        2            ⁡      x        ≤                    |            1              |            +              |            −      2      sin      ⁡              x                    |                    1      +              cos        2            ⁡      x        ≤      3          1      +              cos        2            ⁡      x        ≤  3.            1      −      2      sin      ⁡              x                    1      +              cos        2            ⁡      x        ≥                    |            1              |            −              |            2      sin      ⁡              x                    |                    1      +              cos        2            ⁡      x        ≥            1      −      2        1    =  −  1.Thus,  −  1  ≤  f  (  x  )  ≤  3and our function is indeed boubded.

How can I prove that this function is bounded using the given hint? f(x) = (1-2 sin x)/(1 + cos^2 x),

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