Question

cos 70/sin20+cos 55 cosec 35/tan 5 tan 25 tan 45 tan 65 tan 85,Evaluate it.

Answer 1

cos70°/sin20° + (cos55°.cosec35°)/(tan5°.tan25°.tan65°.tan85°)

we know, sin(90 - θ) = cosθ
so, sin20° = sin(90° -70°) = cos70° ----(1)
cos55° = cos(90° - 35°) = sin35° ------(2)

also tan(90° - θ) = cotθ
so, tan25° = tan(90° - 65°) = cot65° -----(3)
tan5° = tan(90° - 85°) = cot85° -----(4)

from equations (1), (2), (3) and (4),

= cos70°/cos70° + {sin35°. cosec35°}/{cot85°.cot65°.tan45°.tan65°.tan85°}

= 1 + {sin35° × 1/sin35°}/{(tan85°.cot85°) × tan45° × (tan65°.cot65°)}

= 1 + 1/tan45°

= 1 + 1/1 = 1 + 1 = 2 [ans]