Question

(ii) cos 40° cos 20° – sin 40° sin 20°


Hejwooaoe

Uwhejjr

Answer 1

cos40 cos20 - sin40 sin20

= cos( 40 + 20)

= cos 60

= 1/2

Answer 2

Answer:

$\green{\cos \left(40^{\circ \:}\right)\cos \left(20^{\circ \:}\right)-\sin \left(40^{\circ \:}\right)\sin \left(20^{\circ \:}\right)=\frac{1}{2}\quad \begin{pmatrix}\mathrm{Decimal:}&0.5\end{pmatrix}}$

Step-by-step explanation:

$\cos \left(40^{\circ \:}\right)\cos \left(20^{\circ \:}\right)-\sin \left(40^{\circ \:}\right)\sin \left(20^{\circ \:}\right)$

$\gray{\mathrm{Use\:the\:following\:identity}:\quad \cos \left(s\right)\cos \left(t\right)-\sin \left(s\right)\sin \left(t\right)=\cos \left(s+t\right)}$

$\gray{\cos \left(40^{\circ \:}\right)\cos \left(20^{\circ \:}\right)-\sin \left(40^{\circ \:}\right)\sin \left(20^{\circ \:}\right)=\cos \left(40^{\circ \:}+20^{\circ \:}\right)}$

$=\cos \left(40^{\circ \:}+20^{\circ \:}\right)$

$\gray{\mathrm{Simplify}}$

$=\cos \left(60^{\circ \:}\right)$

$\gray{\mathrm{Use\:the\:following\:trivial\:identity}:\quad \cos \left(60^{\circ \:}\right)=\frac{1}{2}}$

$=\frac{1}{2}$