#Trigo

Geometry Level 3

The value of csc ⁡ 1 0 ∘ − 3 sec ⁡ 1 0 ∘ \csc 10^{\circ} - \sqrt3 \sec 10^{\circ} is:

1 1 4 \frac {1}{4} 2 4

Vilakshan Gupta by Vilakshan Gupta , 19, India

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

Zach Abueg
May 28, 2017

csc ⁡ 10 ° − 3 sec ⁡ 10 ° = 1 sin ⁡ 10 ° − 3 cos ⁡ 10 ° = cos ⁡ 10 ° − 3 sin ⁡ 10 ° sin ⁡ 10 ° cos ⁡ 10 ° = 4 1 2 cos ⁡ 10 ° − 3 2 sin ⁡ 10 ° 2 sin ⁡ 10 ° cos ⁡ 10 ° = 4 sin ⁡ 30 ° cos ⁡ 10 ° − cos ⁡ 30 ° sin ⁡ 10 ° sin ⁡ 2 ( 10 ° ) = 4 sin ⁡ ( 30 ° − 10 ° ) sin ⁡ 20 ° = 4 \displaystyle \begin{aligned} \csc 10° - \sqrt{3}\sec 10° & = \frac{1}{\sin 10°} - \frac{\sqrt{3}}{\cos 10°} \\ \\ & = \frac{\cos 10° - \sqrt{3}\sin 10°}{\sin 10°\cos 10°} \\ \\ & = 4 \ \frac{{\color{#3D99F6}{\frac 12}} \cos 10° - {\color{#3D99F6}{\frac{\sqrt{3}}{2}}} \sin 10°}{2\sin10°\cos10°} \\ \\ & = 4 \ \frac{{\color{#3D99F6}{\sin30°}}\cos10° - {\color{#3D99F6}{\cos30°}}\sin10°}{\sin 2(10°)} \\ \\ & = 4 \ \frac{\sin(30° - 10°)}{\sin 20°} \\ \\ & = 4 \end{aligned}

3 Helpful 0 Interesting 0 Brilliant 1 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...