Recall that 2sin(x) cos(x) is actually equal to sin(2x).

We can prove this by expanding sin(2x) to sin(x + x).
sin(x + x) = sin(x) cos(x) + cos(x) sin(x) = 2sinxcosx

Thus, 2sin(x/2)cos(x/2) can be rewritten in the form:
sin(2x/2), and this simplifies down to sinx.

5 0

3 years ago

Find the values of x and y. (look at image) x= y=

scZoUnD [109]

Answer:

helloo…

Step-by-step explanation:

I probably solved it right…

(If you don't understand my writing, I will rewrite it)

5 0

3 years ago

Use this equation to find dy/dx. 3y cos x = x2 + y2

Art [367]

Given: 3y cos x = x² + y²

Define $y' = \frac{dy}{dx}$

Then by implicit differentiation, obtain
3y' cos(x) - 3y sin(x) = 2x + 2y y'
y' [3 cos(x) - 2y] = 2x + 3y sinx)

Answer:
$\frac{dy}{dx} = \frac{2x+3y \, sin(x)}{3cos(x)-2y}$

5 0

3 years ago