If `cos(alpha+beta)sin(gamma+delta)="cos"(alpha-beta)"sin"(gamma-delta)` , prove that `cotalphacotbetacotgamma=cotdelta`

Explanation

`cos (alpha+beta) sin (r+delta)=cos (alpha-beta) sin (r-delta)` then, `because cos (a+b)=cos a cos b-sin a sin b`


`cos (a-b)=cos a cos b+sin a sin b`


`sin (a+b)=sin a cos b+cos a sin b`


`sin (a-b)=sin a cos b-cos a sin b`


Now


`cos (alpha+beta) sin (r+delta)=cos (alpha+beta) sin (r+delta)`


`Rightarrow frac{sin (r +delta)}{sin (r-delta)}=frac{cos (alpha+beta)}{cos (alpha beta)}`


`Rightarrow frac{sin r cos delta+cos r sin delta}{sin r cos delta-cos r sin delta}=frac{cos alpha cos beta+sin alpha cdot sin beta}{cos alpha cos beta-sin alpha sin beta}`


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