Question

Prove that cos(x + y) =cos x cos y -sinx sin y .​

Answer 1

Recall the identity

cos

(

A

+

B

)

=

cos

A

cos

B

−

sin

A

sin

B

Putting

A

=

y

and

B

=

x

−

y

, we get

A

+

B

=

y

+

x

−

y

=

x

and the above identity becomes

cos

y

cos

(

x

−

y

)

−

sin

y

sin

(

x

−

y

)

=

cos

x