buktikan (sec A - cos A)^2 = tan^2 A (1-cos^2 A)

Trigonometry Identity.

From right side to left side.
[tex]\displaystyle \tan^2 A(1-\cos^2 A)^2\\ =(\sec^2 A-1)(1-\cos^2 A)^2\\ =\left ( \frac{1}{\cos^2 A}-1 \right )(1-\cos^2 A)^2\\ =\left ( \frac{1-\cos^2 A}{\cos^2 A} \right )(1-\cos^2 A)^2\\ = \left ( \frac{1-\cos^2 A}{\cos A} \right )^2\\ =\left ( \frac{1}{\cos A}-\cos A \right )^2\\ =(\sec A-\cos A)^2[/tex]
Proved.