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.