Find the value of $x$

Geometry Level 3

$\large \sin 20^\circ \cos 50^\circ = x \sec 10^\circ$ If the real number $x$ satisfying the above equation is of the form $\dfrac {\sqrt {a}}{b}$ , where $a$ and $b$ are integers , and $a$ is square-free, find $a+b$ .

The answer is 11.

1 solution

Sanath Balaji
Jun 1, 2016

sin(20).cos(50)=x.sec(10)

$sin(20).sin(40)=\frac { x }{ sin(80) }$

$sin(20).sin(40).sin(80)=x\\ We\quad Know\quad That,\\ sin(\theta ).sin(60-\theta ).sin(60+\theta )=\frac { sin(3\theta ) }{ 4 } \\ Hence\quad x=sin(60)/4\\ x=\frac { \sqrt [ 2 ]{ 3 } }{ 8 } \\ a+b=11$

Find the value of x x x

The answer is 11.

1 solution

0 pending reports

Find the value of $x$