Question

Evaluate: `cos 58^@/sin 32^@  + sin 22^@/cos 68^@  - (cos 38^@ cosec 52^@)/(tan 18^@ tan 35^@ tan 60^@ tan 72^@ tan 55^@)`

Answer 1

cos 58° = cos (90° – 32°) = sin 32°

sin 22° = sin (90° – 68°) = cos 68°

cos 38° = cos (90 – 52) = sin 52°

tan 18° = cot 72 tan 35° = cot 55°

`=> sin 32^@/sin 32^@ + cos 68^@/cos 68^@ - (sin 52 cosec 52)/(tan 72.cot72 tan 55 cot 55.tan 60)`

`= 1 + 1 - 1/sqrt3 = (2sqrt3-1)/sqrt3 xx sqrt3/sqrt3 = (6 - sqrt3)/3`