cos 80°/sin 10° + cos 59° cosec 31° = 2.

(i) cos 70°/sin 20° + cos 59°/sin 31° – 8 sin² 30° = 0

(ii) cos 80°/sin 10° + cos 59° cosec 31° = 2.

Answer :

(i) cos 70°/sin 20° + cos 59°/sin 31° – 8 sin² 30° = 0

LHS = cos 70°/sin 20° + cos 59°/sin 31° – 8 sin² 30°

= cos 70°/sin (90° – 70°) + cos 59°/sin (90° – 59°) – 8 sin² 30°

sin 30° = ½

= cos 70°/cos 70° + cos 59°/ cos 59° – 8 (1/2)²

= 1 + 1 – (8 × ¼)

= 2 – 2

= 0

= RHS

(ii) cos 80°/sin 10° + cos 59° cosec 31° = 2

LHS = cos 80°/sin 10° + cos 59° cosec 31°

= cos 80°/sin (90° – 80°) + cos 59°/ sin 31°

= cos 80°/ cos 80° + cos 59°/ sin (90° – 59°)

= 1 + cos 59°/ cos 59°

= 1 + 1

= 2

= RHS

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