Question

Evaluate: `(3 cos 55^@)/(7 sin 35^@) -  (4(cos 70 cosec 20^@))/(7(tan 5^@ tan 25^@ tan 45^@ tan 65^@ tan  85^@))`

Answer 1

cos 55° = cos (90° - 35°) = sin 35°

cos 70° = cos (90 – 20) = sin 20°

tan 5 = cot 85° tan 25° = cot 65°

`=> (3 sin 35^@)/(7 sin 35^@) -  (4(sin 20^@ cosec 20^@))/(7(cot 85^@ + tan 85^@ cot 65^@ tan  65^@ tan 45^@))`

`= 3/7 - 4/7 = -1/7`