Find the derivative of sinθcosθ

Assessment: JAMB UTME - Mathematics - 2011 Subject: General Mathematics

Question 1 Report

Find the derivative of $\frac{\sin θ}{\cos θ}$

sec2

θ

tan

θ

cosec

θ

cosec

θ

sec

θ

cosec2

θ

Answer Details

$\frac{\sin θ}{\cos θ}$
$\frac{\cos θ \frac{d (\sin θ)}{d θ} - \sin θ \frac{d (\cos θ)}{d θ}}{\cos^{2} θ}$
$\frac{\cos θ . \cos θ - \sin θ (- \sin θ)}{c o s^{2} θ}$
$\frac{c o s^{2} θ + \sin^{2} θ}{c o s^{2} θ}$
Recall that sin2 $θ$ + cos2 $θ$ = 1
$\frac{1}{\cos^{2} θ}$ = sec2 $θ$