sin 105 degree +cos 105 degree =cos 45 degree

To prove : sin 105° + cos 105° = cos 45°

LHS = sin 105° + cos 105°

= cos 15° – sin 15°  [sin (90° + θ) = cos θ, cos (90° + θ) = – sin θ]

Finding sin 15° and cos 15°: