cot 40°/tan 50° – ½ (cos 35°/sin 55°)

(i) cot 40°/tan 50° – ½ (cos 35°/sin 55°)

(ii) (sin 49°/cos 41°)² + (cos 41°/sin 49°)²

(iii) sin 72°/cos 18° – sec 32°/cosec 58°

(iv) cos 75°/sin 15° + sin 12°/cos 78°– cos 18°/sin 72°

(v) sin 25°/sec 65° + cos 25°/ cosec 65°.

Answer :

(i) cot 40°/tan 50° – ½ (cos 35°/sin 55°)

It can be written as

=1/2

(ii) (sin 49°/cos 41°)² + (cos 41°/sin 49°)²

= 1² + 1²

= 1 + 1

= 2

(iii) sin 72°/cos 18° – sec 32°/cosec 58°

= 1 – 1

= 0

(iv) cos 75°/sin 15° + sin 12°/ cos 78° – cos 18°/sin 72°

= 1 + 1 – 1

= 1

(v) sin 25°/sec 65° + cos 25°/ cosec 65°

= (sin 25° × cos 65°) + (cos 25° × sin 65°)

= [sin 25° × cos (90°– 25°)] + [cos 25° × sin (90° – 25°)]

= (sin 25°× sin 25°) + (cos 25° × cos 25°)

= sin² 25° + cos² 25°

= 1

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