Вычислите: а) cos 105 градусов б) sin 75 градусов в) cig 15 градусов

а)  cos105° =cos(60° +45°) = cos60°*cos45° -sin60°*sin45° = (1/2)*(√2)/2 - (√3)/2 *(√2)/2= (√2)/4 (1-√3). или  cos105° =cos(90°+15°) = - sin15° = -√(1-cos30°)/2 =  -√(1-√3/2)/2 =  -(1/2)√(2-√3) = -(1/2)√((1-√3)²/2) =- (1/2√2)(1-√3)=(√2)/4 (1-√3) . б) sin75° =sin(45° +30°) =sin45°cos30° +cos45°sin30°= 1/√2 *(√3)/2 +(1/√2)*(1/2) = (√3+1)/2√2 =√2(√3+1)/4.  или sin75° =sin(90° -15°) =cos15° =√ ((1+cos30°)/2) =√((1+(√3)/2)/2) = (1/2)√(2+√3)  =(1/2)√( (√3+1)²*1/2) = (√3+1)/2√2 =√2(√3+1)/4. в) ctq15° =ctq(45° - 30°) =(ctq45°ctq30° +1)/(ctq30° -ctq45°)=(√3+1)/(√3 -1)= ((√3+1)²/2 =2+ √3 . или  ctq15° =√((1+cos30°)/(1-cos30°) ) =√(2+√3)/(2-√3) =2+√3.