Question

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

Answer 1

Answer:

see the procedure

Step-by-step 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