Wiskunde Multiple Choice Vraag uit Gricha's Wiskundige Vragenbank

$\frac{1}{\sin^4 15^\circ}-\frac{1}{\cos^4 15^\circ}=$	A. 2
B. 8
C. 16
D. 32
E. 128

$https://latex.codecogs.com/png.image?\inline \LARGE \dpi{110}\frac{1}{\sin^4 15^\circ}-\frac{1}{\cos^4 15^\circ}$	A. 2
	B. 8
	C. 16
	D. 32
	E. 128

$\frac{1}{\sin^4 15^\circ}-\frac{1}{\cos^4 15^\circ}=\frac{\cos^415^\circ-\\\sin^415^\circ}{\sin^415^\circ.\cos^415^\circ}=\frac{(\cos^215^\circ-\sin^215^\circ).(\cos^215^\circ+\sin^215^\circ)}{(\sin15^\circ.\cos15^\circ)^4}\\=\frac{16(\cos^215^\circ-\sin^215^\circ)}{(2\sin15^\circ.\cos15^\circ)^4}=\frac{16.\cos30^\circ}{\sin^430^\circ}=256.\cos30^\circ=256.\frac{\sqrt3}{2}=128\sqrt3$