Question

prove that:sin105°+cos105°=1/√2​

Answer 1

LHS :-

sin 105° + cos 105°

= cos (90° - 105°) + cos 105°

= cos 15° + cos 105°

= cos C + cos D = 2(cos(C+D)/2)(cos(C-D)/2)

= 2cos(120°/2)cos(90°/2)

= 2cos60°cos45°

= 2(1/2)cos45°

= cos45°

= 1/√2

= RHS.