trigonometric equation involving two variablesShow that the equation sec 2 ⁡ θ = 4 x y ( x + y ) 2 is only possible when x = yCan we write it this way : cos 2 ⁡ θ = ( x + y ) 2 4 x y and − 1 ≤ cos ⁡ θ ≤ 1 ⟹ − 1 ≤ ( x + y ) 2 4 x y ≤ 1or − 4 x y ≤ ( x + y ) 2 ≤ 4 x y Please guide...

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trigonometric equation involving two variablesShow that the equation       sec    2    ⁡  θ  =            4      x      y              (      x      +      y              )        2             is only possible when   x  =  yCan we write it this way :      cos    2    ⁡  θ  =            (      x      +      y              )        2                    4      x      y      and  −  1  ≤  cos  ⁡  θ  ≤  1  ⟹  −  1  ≤            (      x      +      y              )        2                    4      x      y        ≤  1or   −  4  x  y  ≤  (  x  +  y      )    2    ≤  4  x  y Please guide...

Samuel Hooper · Accepted Answer

You&#039;re almost there:            (      x      +      y              )        2                            |            4      x      y              |              ≤  1    ⟺        x    2    +  2  x  y  +      y    2    ≤      |    4  x  y      |      ⟺    (  x  −  y      )    2    ≤  0    ⟺    x  =  y

Cortez Clarke · Accepted Answer

Hint: At the step where you change to       cos    2    ⁡  θ, revert back to the old trigonometry definition: the cosine is the ratio of the adjacent side of a right triangle to the hypotenuse of the right triangle.

trigonometric equation involving two variables Show that the equation sec^2 theta = (4xy)/((x+y)^2) is only possible when x=y.

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