Question

How to prove or explain why sin(2x) does not equal 2sin(x) ?

Answer 1

sin 2x =sin (x+x) use sin(A+B)

Answer 2

how would I use the sin(A+B)=sinacosb+cosasinb formula to solve that?

Answer 3

here x=A=B

Answer 4

just use that !

Answer 5

sin(A+B)=sinacosb+cosasinb

A=B=x

Answer 6

So what would A and B be in the equation? 2?

Answer 7

"How to prove or explain why sin(2x) does not equal 2sin(x) ? "
Find a counter example.

Answer 8

A=B=x

Answer 9

sin(2x) is a horizontal stretch of factor 0.5
2sin(x) is a vertical stretch of factor 2

Answer 10

Another way to prove negatives is with an example case that fails. \(2\sin{\frac{\pi}{2}}\ne\sin\pi\)

Answer 11

One good counter example is \(x=90^\circ\).

Answer 12

sin x cos x+cos x sin x=2 sinx cos x is not equal to 2 sin x