#### (i) cos 65°/sin 25° + cos 32°/sin 58° – sin 28° sec 62° + cosec^{2} 30°

#### (ii) sec 29°/ cosec 61° + 2 cot 8° cot 17° cot 45° cot 73° cot 82° – 3 (sin^{2} 38° + sin^{2} 52°).

**Answer :**

**(i)**** cos 65°/sin 25° + cos 32°/sin 58° – sin 28° sec 62° + cosec**^{2} 30°

^{2}30°

= cos 65°/sin (90° – 65°) + cos 32°/sin (90°–32°) – sin 28° sec (90°–28°) + cosec^{2} 30°

= cos 65°/cos 65° + cos 32°/cos 32° – sin 28° cosec 28° + cosec^{2} 30°

cosec 30° = 2

= 1 + 1 – 1 + 4

= 5

**(ii)**** sec 29°/cosec 61° + 2 cot8° cot17° cot45° cot73° cot82° – 3 (sin**^{2} 38° + sin^{2} 52°)

^{2}38° + sin

^{2}52°)

= sec 29°/cosec (90° – 29°) + 2 cot8° cot17° cot45° cot (90°–17°) cot (90°–8°) – 3 [sin^{2}38° + sin^{2} (90°–38°)]

= sec 29°/sec 29° + (2 cot8° cot17° × 1 × tan17° tan8°) – 3 (sin^{2} 38° + cos^{2} 38°)

= 1 + (2 cot 8° tan 8° cot 17° tan 17° × 1) – (3 × 1)

cosec (90° – θ) = sec θ

⇒ cot (90° – θ) = tan θ

⇒ sin^{2} θ + cos^{2} θ = 1

= 1 + (2 × 1 × 1 × 1) – 3

= 1 + 2 – 3

= 0

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