Rumus turunan fungsi trigonometri, yaitu:

1. f(x) = sin x → f'(x) = cos x

2. f(x) = cos x → f'(x) = -sin x

3. f(x) = tan x → f'(x) = sec² x

4. f(x) = cotan x → f'(x) = -cosec² x

5. f(x) = sec x → f'(x) = sec x . tan x

6. f(x) = cosec x → f'(x) = -cosec x . cotan x

Rumus-rumus yang penting dalam pembuktian identitas trigonometri:

1. sin² α + cos² α = 1

2. sin 2α = 2 sin α cos α

3. cos 2α = cos² α - sin² α

⇔ cos 2α = 1 - 2 sin² α

⇔ cos 2α = 2 cos² α - 1

a) y = sinx cosx

Jawab:

Misalkan u = sinx ; u' = cosx

v = cosx ; v' = - sinx

Sehingga,

F'(x) = (uv)' = u'v + uv'

= (cosx)(cosx) + (sinx)(-sinx)

= cos²x + (-sin²x)

= cos²x - sin²x

= cos 2x

b) y = sinx / sinx + cosx

Jawab:

Misalkan u = sinx ; u' = cosx

v = sinx + cosx ; v' = cosx - sinx

Sehingga,

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