Question

Prove :- (cos20° + cos10°) / (cos20° - sin10°) = (root of 3) tan40°

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°)] 
.......................................... sin40° = cos50°] 
= √3 * [(cos70° + sin80°) / (sin80° + cos70°)] 
= √3 
= 1.732050808.

Answer 2

Pls mark as brainliest pls