Wiskunde Multiple Choice Vraag uit Gricha's Wiskundige Vragenbank

(tan 20° + cot 20° ) . sin 40° is gelijk aan	A. 1
B. 2
C. sin 40°
D. sin 20° + cos 20°
E. 0

(tan 20° + cot 20° )(sin 40°) is equal to	A. 1
B. 2
C. sin 40°
D. sin 20° + cos 20°
E. 0

1^ste manier :
$\begin{aligned} & (\tan20^\circ+\cot20^\circ).\sin40^\circ=\left(\frac{\sin20^\circ}{\cos20^\circ}\right)+\left(\frac{\cos20^\circ}{\sin20^\circ}\right).\sin40^\circ\\ & =\frac{\sin^220^\circ+\cos20^\circ}{\cos20^\circ.\sin20^\circ}.\sin40^\circ\\ & =\frac{1}{\cos20^\circ.\sin20^\circ}.\sin40^\circ=\frac{2}{2\sin20^\circ\cos20^\circ}.\sin40^\circ\\ & =\frac{2}{\sin40^\circ}.\sin40^\circ=2\end{aligned}$
2^de manier :
$\\(\tan20^\circ+\cot20^\circ).\sin40^\circ=\\\tan20^\circ.\sin40^\circ+\cot20^\circ.\sin 40^\circ\\=(\tan20^\circ).2\sin20^\circ.\cos20^\circ+(\cot20^\circ).2\sin20^\circ.\cos20^\circ\\=2\sin^220^\circ+2\cos^220^\circ\\=2(\sin^220^\circ+\cos^220^\circ)\\=2$