Question

find the value of cos 10 + sin 20 / cos 20 - sin 10​

Answer 1

(cos10° + sin20°) / (cos20° - sin10°)

= tan60° * (cos60°/sin60°) * [(cos10° + sin20°) / (cos20° - sin10°)]

= tan60° * [(2cos60° cos10° + 2cos60° sin20°) / (2sin60°cos20° - 2sin60° sin10°)]

= √3 * [(cos70° + cos50° + sin80° - sin40°) / (sin80° + sin40° - cos50° + cos70°)]

= √3 * [(cos70° + cos50° + sin80° - cos50°) / (sin80° + cos50° - cos50° + cos70°)]

.......................................[because sin40° = cos50°]

= √3 * [(cos70° + sin80°) / (sin80° + cos70°)]

= √3

= 1.732050808.