Question

Prove the identity cos(x-y)-cos(x+y)=2sinxsiny

Answer 1

see the procedure

Explanation:

we know that

`cos(X - Y) = cosX cosY + sinX sinY\\cos(X + Y) = cosX cosY - sinX sinY`

so

`cos(X - Y)-cos(X + Y)=cosX cosY + sinX sinY-(cosX cosY - sinX sinY)`

`cos(X - Y)-cos(X + Y)=cosX cosY + sinX sinY-cosX cosY + sinX sinY`

`cos(X - Y)-cos(X + Y)=sinX sinY+ sinX sinY`

`cos(X - Y)-cos(X + Y)=2sinX sinY` ----> is verified