Question

${\cos }^3{10}^o+{\cos }^3{110}^o+{\cos }^3{130}^o=$

Answer 1

Given ${\cos }^{3}10+{\cos }^{3}110+{\cos }^{3}130$

We know

${\cos }^{3}x+{\cos }^3(120-x)+{\cos }^3(120+x)=\frac{3}{4}\cos 3x$

here $x=10$

Now,

$={\cos }^{3}10+{\cos }^3(120-10)+{\cos }^3(120+10)$

$=\frac{3}{4}\cos (3\times 10)$

$=\frac{3}{4}\cos \left(30\right)$

$=\frac{3}{4}\times \frac{\sqrt{3}}{2}$

$=\frac{3\sqrt{3}}{8}$