2sin(4t)[(cos(3/2)x)(cos(5x/2)-sin((15/4)x)]+x

What is the question? Is there an equal sign in the above? Are there two variables, t and x?

to bobpursely: i need to simplify the expression using trig identities. and no i meant for there to only be x

To simplify the given expression, we'll break it down step-by-step.

First, let's simplify the expression inside the square brackets.

(cos(3/2)x)(cos(5x/2) - sin((15/4)x))

To simplify further, we'll use the trigonometric identity cos(A)cos(B) - sin(A)sin(B) = cos(A + B).

Therefore, we can rewrite the expression as:

cos((3/2)x + (5x/2)) = cos(4x)

Now, let's substitute this simplified expression back into the original equation:

2sin(4t)[cos(4x)] + x

This gives us the final simplified expression:

2sin(4t)cos(4x) + x

That's it! The original expression, 2sin(4t)[(cos(3/2)x)(cos(5x/2) - sin((15/4)x))] + x, simplifies to 2sin(4t)cos(4x) + x.