*** QuickLaTeX cannot compile formula:
\displaystyle \cos \left( {{x}_{1}}-{{x}_{2}} \right)=\cos {{x}_{1}}\cdot \cos {{x}_{2}}+\sin {{x}_{1}}\cdot \sin {{x}_{2}}<pre class="ql-errors">*** QuickLaTeX cannot compile formula:
\[latex \displaystyle \cos 120{}^\text{o}$ e shkruajmë si $latex \displaystyle \cos \left( 180{}^\text{o}-60{}^\text{o} \right)$ dhe do të kemi:
$latex \displaystyle \cos \left( 180{}^\text{o}-60{}^\text{o} \right)=\cos 180{}^\text{o}\cdot \cos 60{}^\text{o}+\sin 180{}^\text{o}\cdot \sin 60{}^\text{o}$
$latex \displaystyle =-1\cdot \frac{1}{2}+0\cdot \frac{\sqrt{2}}{2}$
$latex \displaystyle =-1\cdot \frac{1}{2}+0\cdot \frac{\sqrt{2}}{2}=-\frac{1}{2}$.
</div>
<!--Ads2-->
<h2 style="text-align: center;"><span style="color: #0000ff;"><strong>Formula për cos(x<sub>1</sub>+x<sub>2</sub>)</strong></span></h2>
Në identitetin që kemi për cos(x<sub>1</sub>+x<sub>2</sub>), zëvëndësojmë $latex \displaystyle {{x}_{2}}$ me $latex \displaystyle \left( -{{x}_{2}} \right)$.
Do të kemi:
<div style="overflow-x: auto;">$latex \displaystyle \cos \left( {{x}_{1}}+{{x}_{2}} \right)=\cos {{x}_{1}}\cdot \cos {{x}_{2}}-\sin {{x}_{1}}\cdot \sin {{x}_{2}}$, sepse $latex \displaystyle \cos \left( -{{x}_{2}} \right)=\cos \left( {{x}_{2}} \right)$ dhe $latex \displaystyle \sin \left( -{{x}_{2}} \right)=-\sin \left( {{x}_{2}} \right)$.</div>
<h3> </h3>
<h3> </h3>
<h3> </h3>
<h3 style="text-align: center;"><span style="text-decoration: underline; color: #ff0000;"><strong>Ushtrimi 2</strong></span></h3>
Të njehësohet $latex \displaystyle \cos 105{}^\text{o}$
<h4 style="text-align: center;"><span style="color: #008000;"><strong>Zgjidhje</strong></span></h4>
<div style="overflow-x: auto;">$latex \displaystyle \cos 105{}^\text{o}$ e shkruajmë si $latex \displaystyle \cos \left( 60{}^\text{o}+45{}^\text{o} \right)$ dhe zbatojmë formulën për gjetjen e shumës së kosinuseve:$latex \displaystyle \cos \left( {{x}_{1}}+{{x}_{2}} \right)=\cos {{x}_{1}}\cdot \cos {{x}_{2}}-\sin {{x}_{1}}\cdot \sin {{x}_{2}}$</div>
Bëjmë zëvëndësimet:
<div style="overflow-x: auto;">$latex \displaystyle \cos \left( 60{}^\text{o}+45{}^\text{o} \right)=\cos 60{}^\text{o}\cdot \cos 45{}^\text{o}-\sin 60{}^\text{o}\cdot \sin 45{}^\text{o}\]
*** Error message:
Display math should end with $$.
leading text: \[latex \displaystyle \cos 120{}^\text{o}$ 
</pre>latex \displaystyle =\frac{1}{2}\cdot \frac{\sqrt{2}}{2}-\frac{\sqrt{3}}{2}\cdot \frac{\sqrt{2}}{2}

*** Error message:
Missing $ inserted.
leading text: \displaystyle

*** QuickLaTeX cannot compile formula:
\displaystyle \cos \left( 90{}^\text{o}-{{x}_{1}}-{{x}_{2}} \right)=\cos \left( 90{}^\text{o}-{{x}_{1}} \right)\cdot \cos {{x}_{2}}+\sin \left( 90{}^\text{o}-{{x}_{1}} \right)\cdot \sin {{x}_{2}}<pre class="ql-errors">*** QuickLaTeX cannot compile formula:
\[latex \displaystyle \cos \left[ 90{}^\text{o}-\left( {{x}_{1}}-{{x}_{2}} \right) \right]=\sin {{x}_{1}}\cdot \cos {{x}_{2}}+\cos {{x}_{1}}\cdot \sin {{x}_{2}}$, pra:
$latex \displaystyle \sin \left( {{x}_{1}}+{{x}_{2}} \right)=\sin {{x}_{1}}\cdot \cos {{x}_{2}}+\cos {{x}_{1}}\cdot \sin {{x}_{2}}$.
</div>
Kemi pasur parasysh faktin që $latex \displaystyle \sin \left( 90{}^\text{o}-\alpha  \right)=\cos \alpha $.
<h3 style="text-align: center;"><span style="text-decoration: underline; color: #ff0000;"><strong>Ushtrimi 3</strong></span></h3>
Të gjendet $latex \displaystyle \sin 75{}^\text{o}$.
<h4 style="text-align: center;"><span style="color: #008000;"><strong>Zgjidhje</strong></span></h4>
Shkruajmë $latex \displaystyle \sin 75{}^\text{o}=\sin \left( 45{}^\text{o}+30{}^\text{o} \right)$.
Zbatojmë formulën për shumën e sinuseve:
<div style="overflow-x: auto;">$latex \displaystyle \sin \left( 45{}^\text{o}+30{}^\text{o} \right)=\sin 45{}^\text{o}\cdot \cos 30{}^\text{o}+\cos 45{}^\text{o}\cdot \sin 30{}^\text{o}\]
*** Error message:
Display math should end with $$.
leading text: ...}_{2}}+\cos {{x}_{1}}\cdot \sin {{x}_{2}}$,
</pre>latex \displaystyle =\frac{\sqrt{2}}{2}\cdot \frac{\sqrt{3}}{2}+\frac{\sqrt{2}}{2}\cdot \frac{1}{2}

*** Error message:
Missing $ inserted.
leading text: \displaystyle

.