Question

Prove that :
sin(x+1)x cos(n-1)x - cos(x+1)x sin(n-1)x = sin²x ​

Answer 1

Answer:

Taking L.H.S

we know that

coz (A- B) =coz a coz b+ sin A sin B

Here

A =(n+ 1)×

B=(n+ 2)×

Hence

sin(n+1)x sin(n+2)x+ coz(n+1)x coz(n+2)x

=coz[(n+1)-(n+2)x]

=coz [nx+ x -nx -2x]

=coz[nx- nx- x- 2x]

=coz(0-x)

=coz(-x)

=coz x. =(coz(-x)=coz x)

=R.H.S

Hence

L.H.S=R.H.S

Hence proved.