Question

Evaluate:
(i) $\frac{\sin 18^{\circ }}{\cos {72}^{\circ }}$

(ii) $\frac{\tan {26}^{\circ }}{\cot {64}^{\circ }}$

(iii) $\cos {48}^{\circ }-\sin {42}^{\circ }$

(iv) $\csc {31}^{\circ }-\sec {59}^{\circ }$

Answer 1

(i) $\frac{\sin {18}^o}{\cos {72}^o}=\frac{\sin (90-72{)}^o}{\cos {72}^o}=\frac{\cos {72}^o}{\cos {72}^o}=1$

Hence, the value is $1$

(ii) $\frac{\tan {26}^o}{\cot {64}^o}=\frac{\tan (90-64{)}^o}{\cot {64}^o}=\frac{\cot {64}^o}{\cot {64}^o}=1$

Hence, the value is $1$

(iii) $\cos {48}^o-\sin {42}^o$

$=\cos (90-42{)}^o-\sin {42}^o$

$=\sin {42}^o-\sin {42}^o$

$=0$

Hence, the value is $0$

(iv) $\csc {31}^o-\sec {59}^o$

$=\csc (90-59{)}^o-\sec {59}^o$

$=\sec {59}^o-\sec {59}^o$

$=0$

Hence, the value is $0$