Wiskunde Multiple Choice Vraag uit Gricha's Wiskundige Vragenbank

De afgeleide van tan x − cot x is	A. 1
	B. 2
	C. $\large\boldsymbol{\frac {1} {\cos 2x} }$
	D. $\large\boldsymbol{\frac {1} {(\sin x.\,\cos x)^2} }$
	E. $\large\boldsymbol{-\:\frac {1} {\sin^2x\,.\,\cos^2x} }$

[ 5-0465 - op net sinds 23.12.14-(E)-30.10.2023 ]

Translation in E N G L I S H

What is the derivative of tan x − cot x ?	A. 1
	B. 2
	C. $\boldsymbol{\frac {1} {\cos 2x} }$
	D. $\boldsymbol{\frac {1} {(\sin x.\,\cos x)^2} }$
	E. $\boldsymbol{-\:\frac {1} {\sin^2x\,.\,\cos^2x} }$

Oplossing - Solution

$\\D\, (\tan x - \cot x)=\frac{1}{cos^2 x}+\frac{1}{\sin^2x} =\frac{sin^2x + cos^2 x }{cos^2 x\cdot sin^2x } =\frac{1}{cos^2 x\cdot sin^2x } =\frac{1}{(\sin x\cdot \cos x )^2}$