Question

Find the value of the following expression.
$\frac{cos{70}^{\circ }}{sin{20}^{\circ }}+\frac{cos{59}^{\circ }}{sin{31}^{\circ }}-8si{n}^2{30}^{\circ }$

• A. 1
• B. -1
• C. 0.0
• D. 2

Answer 1

The correct option is C 0.0

We know that,
$cos\theta =sin({90}^{\circ }-\theta ).$
So, $(\cos {70}^{\circ }=sin({90}^{\circ }-{70}^{\circ })=sin{20}^{\circ },cos{59}^{\circ }=sin({90}^{\circ }-{59}^{\circ })=sin{31}^{\circ }$ and $sin{30}^{\circ }=\frac{1}{2})$

By substituting these values, we get,
$\frac{cos{70}^{\circ }}{sin{20}^{\circ }}+\frac{cos{59}^{\circ }}{sin{31}^{\circ }}-8si{n}^2{30}^{\circ }=\frac{sin{20}^{\circ }}{sin{20}^{\circ }}+\frac{sin{31}^{\circ }}{sin{31}^{\circ }}-8(\frac{1}{2}{)}^2$

$=1+1-8\times \frac{1}{4}$
$=2-2=0$

So, $\frac{cos{70}^{\circ }}{sin{20}^{\circ }}+\frac{cos{59}^{\circ }}{sin{31}^{\circ }}-8si{n}^2{30}^{\circ }=0$