sin105^@ + cos105^@sin105∘+cos105∘
sin(60^@+45^@) + cos(60^@+45^@) sin(60∘+45∘)+cos(60∘+45∘)
Sum identities:
sin(alpha +beta) = sin(alpha)cos(beta) +cos(alpha)sin(beta)sin(α+β)=sin(α)cos(β)+cos(α)sin(β)
cos(alpha +beta) = cos(alpha)cos(beta) -sin(alpha)sin(beta)cos(α+β)=cos(α)cos(β)−sin(α)sin(β)
sin60^@ = sqrt3/2sin60∘=√32
sin45^@=sqrt2/2sin45∘=√22
cos60^@=1/2cos60∘=12
cos45^@=sqrt2/2cos45∘=√22
(sqrt3/2*sqrt2/2+1/2*sqrt2/2) + (1/2*sqrt2/2 -sqrt3/2*sqrt2/2 ) = 1/sqrt2(√32⋅√22+12⋅√22)+(12⋅√22−√32⋅√22)=1√2