Question

Find the value of: $\frac{\cos {70}^{\circ }}{\sin {20}^{\circ }}+\frac{\cos {59}^{\circ }}{\sin {31}^{\circ }}+\frac{\cos \theta }{\sin (90-\theta )}-8{\cos }^2{60}^{\circ }$

• A. 1
• B. 5
• C. 9
• D. 14

Answer 1

The correct option is A 1

$\frac{\cos {70}^{\circ }}{\sin {20}^{\circ }}+\frac{\cos {59}^{\circ }}{\sin {31}^{\circ }}+\frac{\cos \theta }{\sin (90-\theta )}-8{\cos }^2{60}^{\circ }$

$=\frac{\cos (90-20{)}^{\circ }}{\sin {20}^{\circ }}+\frac{\cos (90-31{)}^{\circ }}{\sin {31}^{\circ }}+\frac{\cos \theta }{\cos \theta }-8{\left(\frac{1}{2}\right)}^2$

$=\frac{\sin {20}^{\circ }}{\sin {20}^{\circ }}+\frac{\sin {31}^{\circ }}{\sin {31}^{\circ }}+1-2$

$=1+1+1-2$

$=1$