diketahui nilai cotan α + cos α = x dan cotan α - cos α = y. nilai (x² - y²)???

Bab TrigonometriMatematika SMA Kelas X
x = cotan a + cos a
y = cotan a - cos a

x² - y² = (x + y) (x - y)         
          = (cotan a + cos a + cotan a - cos a) (cotan a + cos a - cotan a + cos a)         
          = 2 . cotan a . 2 . cos a         
          = 4 . cos a . cotan a

[tex]x^{2}-y^{2}=(x+y)(x-y)[/tex]
[tex]=(\cot{a}+\cos{a}+\cot{a}-\cos{a})(\cot{a}+\cos{a}-\cot{a}+\cos{a})[/tex]
[tex]=(2\cot{a})(2\cos{a})[/tex]
[tex]=4\cot{a}\cos{a}[/tex]

[tex]xy=(\cot{a}+\cos{a})(\cot{a}-\cos{a})[/tex]
[tex]=(\cot{a})^{2}-(\cos{a})^{2}[/tex]
[tex]=\frac{(\cos{a})^{2}}{(\sin{a})^{2}}-(\cos{a})^2{2}[/tex]
[tex]=(\cos{a})^2*(\frac{1}{(\sin{a})^{2}}-1)[/tex]
[tex]=(\cos{a})^2*\frac{(1-(\sin{a})^{2})}{(\sin{a})^{a}}[/tex]
[tex]=\frac{(\cos{a})^{4}}{(\sin{a})^{2}}[/tex]

[tex]\sqrt{xy}=\sqrt{\frac{(\cos{a})^{4}}{(\sin{a})^{2}}}=\frac{(\cos{a})^{2}}{\sin{a}}[/tex]

[tex]x^{2}-y^{2}=4\frac{\cos{a}}{\sin{a}}*\cos{a}[/tex]
[tex]=4\frac{(cos{a})^{2}}{\sin{a}}[/tex]
[tex]=4\sqrt{xy}[/tex]