Question 1151108


Use the trigonometric identities to expand and simplify if possible.
For: 

{{{(1-cos(D))/(sin(D)+1)}}}-> cannot be simplified



{{{sin(270-A)}}} =  ...........Use the following identity : {{{sin (s-t)=-cos  (s)*sin(t )+ cos(t)*sin(s)}}}

{{{sin(270-A) =- cos (270) *sin(A)+ cos(A)*sin(270)}}}...........since {{{cos(270)=0 }}}and {{{sin(270)=-1}}}, we have

{{{sin(270-A) =- 0*sin  (A )+ cos (A ) *(-1)}}}

{{{sin(270-A) =0- cos (A ) }}}

{{{sin(270-A) =- cos (A ) }}}


for next one use identities above

{{{cos(B+270)=cos(270)cos(B) - sin(270) sin(B)}}}

{{{cos(B+270)=0* cos(B) -(-1) sin(B)}}}

{{{cos(B+270)= sin(B)}}}



{{{tan(C+225)}}}=............Use the following identity : {{{tan(a)=sin(a)/cos(a)}}}

{{{tan(C+225)=sin(C+225)/cos(C+225)}}}

{{{tan(C+225)=(sin(225) cos(C) + cos(225) sin(C))/ (cos(225) cos(C) - sin(225) sin(C))}}}

since {{{sin(225)=-1/sqrt(2) }}}and  {{{cos(225)=-1/sqrt(2)}}}, we have


{{{tan(C+225)=(-(1/sqrt(2)) cos(C) + (-1/sqrt(2)) sin(C))/ (-(1/sqrt(2)) cos(C) - (-1/sqrt(2)) sin(C))}}}

{{{tan(C+225)=(-(1/sqrt(2))( cos(C) +  sin(C)))/ (-(1/sqrt(2)) (cos(C) -  sin(C)))}}}

{{{tan(C+225)=(-cross((1/sqrt(2)))( cos(C) +  sin(C)))/ (-cross((1/sqrt(2))) (-cos(C) +  sin(C)))}}}

{{{tan(C+225)=( sin(C)+ cos(C)  )/  (sin(C) -  cos(C))}}}