Wiskunde Multiple Choice Vraag uit Gricha's Wiskundige Vragenbank

tan x − cot x is gelijk aan _{(x is geen veelvoud van 90°)}	A. \(\small\boldsymbol{-2\cot 2x }\)
	B. \(\boldsymbol{\frac {2} {\sin 2x} }\)
	C. \(\boldsymbol{\cot 2x }\)
	D. \(\boldsymbol{\frac {1} {2\sin 2x} }\)
	E. \(\small\boldsymbol{2\cot 2x }\)

[ 5-2177 - op net sinds 22.1.2020-(E)-6.8.2024 ]

Translation in E N G L I S H

tan x − cot x =	A. \(\small\boldsymbol{-2\cot 2x }\)
	B. \(\boldsymbol{\frac {2} {\sin 2x} }\)
	C. \(\boldsymbol{\cot 2x }\)
	D. \(\boldsymbol{\frac {1} {2\sin 2x} }\)
	E. \(\small\boldsymbol{2\cot 2x }\)

Oplossing - Solution

$\ \\tan x-\cot x=\frac{\sin x}{\cos x}-\frac{\cos x}{\sin x}=\frac{\sin^2 x-\cos^2 x}{\sin x.\cos x}$

$=-\,\frac{\cos 2x}{\sin x.\cos x}\\\;=-\,\frac{2.\cos{2x}}{\sin{2x}}=-\,2\cot{2x}$

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