Cos(pi/2-x)-sin3x+sin5x=0

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вопрос

To simplify the given expression, we can use the following trigonometric identities:

Now, let's simplify the given expression step by step:

Cos(pi/2 - x) - sin(3x) + sin(5x)

Using the cos(a - b) identity:
cos(pi/2 - x) = cos(pi/2)cos(x) + sin(pi/2)sin(x)
cos(pi/2) = 0
sin(pi/2) = 1

Therefore, cos(pi/2 - x) = 0cos(x) + 1sin(x) = sin(x)

Now the expression becomes:
sin(x) - sin(3x) + sin(5x)

Next, we use the sin(a + b) identity:
sin(5x) = sin(3x + 2x) = sin(3x)cos(2x) + cos(3x)sin(2x)

Now, the expression becomes:
sin(x) - sin(3x) + sin(3x)cos(2x) + cos(3x)sin(2x)

Since sin(3x) - sin(3x) = 0, the expression simplifies to:
sin(x) + cos(3x)sin(2x)

Thus, the simplified expression is sin(x) + cos(3x)sin(2x).