Sin5x cos2x + cos5x sin2x=
It matches the pattern of
sin(A+B) = sinAcosB + cosAsinB
sin5x cos2x + cos5x sin2x
= sin(5x+2x)
= sin (7x)
To simplify the given expression:
Step 1: Apply the product-to-sum formula: sin(A + B) = sinA cosB + cosA sinB
Sin5x cos2x + cos5x sin2x
= sin(5x + 2x)
Step 2: Apply the angle addition formula: sin(A + B) = sinA cosB + cosA sinB
= sin(7x)
Therefore, the simplified form of the expression sin5x cos2x + cos5x sin2x is sin(7x).
To simplify the given expression Sin5x cos2x + cos5x sin2x, we can use the trigonometric identity that states:
sin(a + b) = sin(a)cos(b) + cos(a)sin(b)
Applying this identity, we can rewrite the expression as:
sin(5x + 2x)
Now, we can simplify this expression by using another trigonometric identity:
sin(a + b) = sin(a)cos(b) + cos(a)sin(b)
Using this identity, we get:
sin(7x)
Therefore, Sin5x cos2x + cos5x sin2x simplifies to sin(7x).