Question

cos 45º cos 30° +sin 45° sin 30°​

Answer 1

Answer:

1 upon 2root 2 +3 root 2

Step-by-step explanation:

please mark as brainlist hope u will mark as I help u

Answer 2

Answer:

$\displaystyle\blue{\cos \left(45^{\circ \:}\right)\cos \left(30^{\circ \:}\right)+\sin \left(45^{\circ \:}\right)\sin \left(30^{\circ \:}\right)=\frac{\sqrt{6}+\sqrt{2}}{4}\quad \begin{pmatrix}\mathrm{Decimal:}&0.96593\dots \end{pmatrix}}$

Step-by-step explanation:

$\cos \left(45^{\circ \:}\right)\cos \left(30^{\circ \:}\right)+\sin \left(45^{\circ \:}\right)\sin \left(30^{\circ \:}\right)$

$\displaystyle\gray{\mathrm{Use\:the\:following\:trivial\:identity}:\quad \cos \left(45^{\circ \:}\right)=\frac{\sqrt{2}}{2}}$

$\displaystyle\gray{\mathrm{Use\:the\:following\:trivial\:identity}:\quad \cos \left(30^{\circ \:}\right)=\frac{\sqrt{3}}{2}}$

$\displaystyle\gray{\mathrm{Use\:the\:following\:trivial\:identity}:\quad \sin \left(45^{\circ \:}\right)=\frac{\sqrt{2}}{2}}$

$\displaystyle\gray{\mathrm{Use\:the\:following\:trivial\:identity}:\quad \sin \left(30^{\circ \:}\right)=\frac{1}{2}}$

$\displaystyle=\frac{\sqrt{2}}{2}\cdot \frac{\sqrt{3}}{2}+\frac{\sqrt{2}}{2}\cdot \frac{1}{2}$

$\displaystyle\black{\frac{\sqrt{2}}{2}\cdot \frac{\sqrt{3}}{2}+\frac{\sqrt{2}}{2}\cdot \frac{1}{2}}$

$\displaystyle\gray{\frac{\sqrt{2}}{2}\cdot \frac{\sqrt{3}}{2}=\frac{\sqrt{6}}{4}}$

$\displaystyle\gray{\frac{\sqrt{2}}{2}\cdot \frac{1}{2}=\frac{\sqrt{2}}{4}}$

$\displaystyle=\frac{\sqrt{6}}{4}+\frac{\sqrt{2}}{4}$

$\displaystyle\gray{\mathrm{Apply\:rule}\:\frac{a}{c}\pm \frac{b}{c}=\frac{a\pm \:b}{c}}$

$\displaystyle=\frac{\sqrt{6}+\sqrt{2}}{4}$