Antiderivative - Trigonometric Functions

Submitted by michaela.bailova on Sat, 11/30/2024 - 00:05

SubArea:

Project ID:

7500020172

Question:

Create matching triples, each containing a function

f

, an algebraically modified form of

f

, and an antiderivative

F

f

Header 1:

Function

f

Header 2:

Function

f

after algebraic modification

Header 3:

Antiderivative

F

Text 11:

f (x) = \frac{1}{\sin^{2} x \cos^{2} x}

Text 21:

f (x) = \frac{\sin^{2} x + \cos^{2} x}{\sin^{2} x \cos^{2} x}

Text 31:

F (x) = tg x - cotg x

Text 12:

f (x) = \frac{\cos 2 x}{\sin x + \cos x}

Text 22:

f (x) = \frac{\cos^{2} x - \sin^{2} x}{\sin x + \cos x}

Text 32:

F (x) = \sin x + \cos x

Text 13:

f (x) = \frac{\cos 2 x}{\sin^{2} x \cos^{2} x}

Text 23:

f (x) = \frac{\cos^{2} x - \sin^{2} x}{\sin^{2} x \cos^{2} x}

Text 33:

F (x) = - cotg x - tg x

Text 14:

f (x) = \frac{1 + \cos 2 x}{2 \sin^{2} x \cos^{2} x}

Text 24:

f (x) = \frac{1 + \cos^{2} x - \sin^{2} x}{2 \sin^{2} x \cos^{2} x}

Text 34:

F (x) = - cotg x

Text 15:

f (x) = \frac{1 + \sin 2 x}{\sin x + \cos x}

Text 25:

f (x) = \frac{\sin^{2} x + \cos^{2} x + 2 \sin x \cos x}{\sin x + \cos x}

Text 35:

F (x) = - \cos x + \sin x

Text 16:

f (x) = \frac{2 tg x}{\sin 2 x}

Text 26:

\frac{2 \frac{\sin x}{\cos x}}{2 \sin x \cos x}

Text 36:

F (x) = tg x

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