Grammar is as important in mathematics as in any language!

In order to be clear with your intent, you needed to write it as

3*sin^2(x) + 7*sin(x) = cos^2(x) - 4

and

4*sin^2(x) + 7*sin(x) + 3 = 0

or something similar (most important: notice the ^2 to denote squares)

To show you can get from the first to the second, just use

cos^2(x) = 1 - sin^2(x)

to replace the cos^2(x) in the first equation.

I guess you mean

show that 3*sin(2x) + 7*sin(x) = cos(2x) - 4, and

show that 4*sin(2x) + 7*sin(x) + 3 = 0. ???

The latter statement is certainly FALSE, as substituting x = 0 will show.

The former statement is also FALSE, as substituting x = 0 will show.

My guess is that you left out part of the question.