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Q1. Evaluate :
(i) \( \frac{sin18°}{cos72°} \)

(ii) \( \frac{tan26°}{cot64°} \)

(iii) \( cos 48° – sin 42° \)

(iv) \( cosec 31° – sec 59°\)

Answer :


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

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

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

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