Question

Is cos 15* = root 3 +1/ 2 root 2 ? please explain step by step...

Answer 1

$\textbf{using}$

$\boxed{\bf\,cos(A-B)=cos\,A\,cos\,B+sin\,A\,sin\,B}$

$\text{Take A=45^{\circ},\,B=30^{\circ} }$

$cos(45^{\circ}-30^{\circ})=cos45^{\circ}cos30^{\circ}+sin45^{\circ}sin30^{\circ}$

$\implies\displaystyle\cos\,15^{\circ}={\frac{1}{\sqrt2}}\times{\frac{\sqrt3}{2}}+{\frac{1}{\sqrt2}}\times{\frac{1}{2}}$

$=\displaystyle\frac{\sqrt{3}}{2{\sqrt2}}+\frac{1}{2{\sqrt2}}$

$=\displaystyle\frac{{\sqrt3}+1}{2{\sqrt2}}$

$\implies\displaystyle\boxed{\bf\,cos15^{\circ}=\frac{{\sqrt3}+1}{2{\sqrt2}}}$

Answer 2

Step-by-step explanation:

we know that, (1-cos2A) =2cos²A

Hence, (1-cos2×15°)=2cos²15°

»(1-cos30°)/2=cos²15°

»(1-√3/2)/2=cos²15°

»(2-√3)/4=cos²15°

»√(2-√3)/√4=cos15°

Therefore, √(2-√3)/2=cos15°, I hope it is helpful to you