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[tex]\displaystyle \cos\frac12a=\sqrt{\frac{2x+1}{4x}}\\\sqrt{\frac{1+\cos a}{2}}=\sqrt{\frac{1+\frac1{2x}}{2}}\\\therefore\\\cos a=\frac1{2x}\\\sin a=\sqrt{1-\frac{1}{4x^2}}\\\\\cot a=\frac{\cos a}{\sin a}\\\cot a=\frac{\frac1{2x}}{\sqrt{1-\frac{1}{4x^2}}}\\\cot a=\sqrt{\frac{\frac1{4x^2}}{\frac{4x^2-1}{4x^2}}}\\\boxed{\boxed{\cot a=\sqrt{\frac{1}{4x^2-1}}}}[/tex]

Bab Trigonometri
Matematika SMA kelas XI

misal,x = p
cos (a/2) = √((2p + 1)/4p)
cos (a/2) = √((2p / 2p) + (1/2p)) / 2)
cos (a/2) = √((1 + (1/2p))/2)
 
cos a = 1/2p → x/r

y = √(r² - x²)
y = √((2p)² - 1²)
y = √(4p² - 1)

cot a = x/y
cot a = 1/√(4p² - 1)
cot a = √(1 / (4x² - 1))