Question

Evaluate without using trigonometric tables
${\cos }^2{26}^{\circ }+\cos {64}^{\circ }\sin {26}^{\circ }+\frac{\tan {36}^{\circ }}{\cot {54}^{\circ }}$

Answer 1

${\cos }^2{26}^{\circ }+\cos {64}^{\circ }\sin {26}^{\circ }+\frac{\tan {36}^{\circ }}{\cot {54}^{\circ }}={\cos }^2{26}^{\circ }+\cos ({90}^{\circ }-{26}^{\circ })\sin {26}^{\circ }+\frac{\tan {36}^{\circ }}{\cot ({90}^{\circ }-{36}^{\circ })}$

$={\cos }^2{26}^{\circ }+\sin {26}^{\circ }\sin {26}^{\circ }+\frac{\tan {36}^{\circ }}{\tan {36}^{\circ }}$

$={\cos }^2{26}^{\circ }+{\sin }^2{26}^{\circ }+1$

$=1+1$

$=2$