Wiskunde Multiple Choice Vraag uit Gricha's Wiskundige Vragenbank

tan²30°. sin²45° is gelijk aan	A. \(\frac16\)
B. \(\frac32\)
C. \(\frac23\)
D. \(\frac14\)
E. 6

tan²30°. sin²45° is equal to	A. $\frac16$
	B. $\frac32$
	C. $\frac23$
	D. $\frac14$
	E. 6

1^ste manier :
$\\\tan^2\!30^\circ\cdot\sin^2\!45^\circ=(\tan 30^\circ)^2\cdot(\sin 45^\circ)^2=\left(\frac{\sqrt3}{3}\!\right)^2.\left(\frac{\sqrt2}{2}\right)^2=\frac39\cdot\frac24=\frac13\cdot\frac12=\frac16$ 2^de manier :
$\\\tan^230^\circ\cdot\sin^2 45^\circ=\left(\tan 30^\circ\cdot\sin 45^\circ\right)^2=\left(\frac{\sqrt3}{3}\cdot\frac{\sqrt2}{2}\right)^2=\left(\frac{\sqrt6}{6}\right)^2=\frac{6}{36}=\frac16$