Cos 10 + sin20/
Cos20 - sin10
Answers
Answer:
1.732050808
Step-by-step explanation:
(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.
Answer:
Step-by-step explanation:
(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.