Evaluate :
(i) \( \frac{sin18°}{cos72°} \)

(ii) \( \frac{tan26°}{cot64°} \)

(iii) \( cos 48° – sin 42° \)

(iv) \( cosec 31° – sec 59°\)

(i) \( \frac{sin18°}{cos72°} \ \)
\( = \ \frac{sin(90°- 72)}{cos72°} \)
\( = \ \frac{cos72°}{cos72°} \ = \ 1 \) [\(\because \) \( sin(90° - \theta) \ = \ cos\theta \) ]


(ii) \( \frac{tan26°}{cot64°} \ \)
\( = \ \frac{tan(90° - 64°)}{cot64°} \)
\( = \ \frac{cot64°}{cot64°} \ = \ 1\) [\(\because \) \( tan(90° - \theta) \ = \ cot\theta \) ]


(iii) \( cos48° – sin42° \ \)
\( = \ cos (90° – 42°) – sin 42° \)
\( = \ sin 42° – sin 42° = 0 \) [\(\because cos(90° - \theta) \ = \ sin\theta \) ]


(iv) \( cosec 31° – sec 59° \ \)
\( = \ cosec (90° – 59°) – sec 59° \)
\( = \ sec59° - sec59° \ = \ 0\) [\( \because cosec(90° - \theta) \ = \ sec\theta \) ]