Precalculus Solutions | Expert Assistance for Problems & Examples

$lim_{x \to 0} \frac{(\sin {4 x}) (- \cos {x})}{x}$ without l'Hôpital's Rule?

resaplaha7dl 2022-03-30

Proving Trig/Calc Identity $\frac{1}{1 - \sin (x)} = \frac{1 + \sin x}{{\cos (x)}^{2}}$

Jazmyn Holden 2022-03-30

Proving the identity $\frac{1}{\tan x} + \tan x = \frac{1}{\sin x \cos x}$
And here's what I've solved for:
$RHS = \frac{1}{\frac{\sin (x)}{\cos (x)}} + \frac{\sin (x)}{\cos (x)} = \frac{\cos x}{\sin x} + \frac{\sin (x)}{\cos (x)}$
Then, I get stuck. The answers section says the next step should be:
$\frac{\cos^{2} (x) + \sin^{2} (x)}{\sin (x) \cdot \cos (x)} = RHS$

sexoagotadorogyr 2022-03-30

Proving that $\sin (z + w) = \sin (w) \cos (z) + \sin (z) \cos (w)$ using complex exponentials

Harold Hoover 2022-03-30

Proving $1 + \tan^{2} (x) = \sec^{2} (x)$

Rex Maxwell 2022-03-30

Proving $\tan (\frac{a + b}{2}) = \frac{\sin a + \sin b}{\cos a + \cos b}$

svrstanojpkqx 2022-03-30

Prove trigonometric equivalence
$\sin x + \sin y = 2 \sin (\frac{x + y}{2}) \cos (\frac{x - y}{2})$

Ashleigh Shaffer 2022-03-30

Prove the identity
$\cos \frac{x}{2} \cdot \cos \frac{x}{4} \cdot \cos \frac{x}{8} = \frac{\sin x}{8 \sin \frac{x}{8}}$

plastikffxi117h 2022-03-30

Prove the inequalities
$1 - \frac{x^{2}}{2} \leq \cos (x) \leq 1 - \frac{x^{2}}{2} + \frac{x^{4}}{24}$

Aleah Choi 2022-03-30

Series $\sum_{k = 1}^{n} \frac{\tan \frac{x}{2^{k}}}{2^{k - 1} \cos \frac{x}{2^{k - 1}}}$

London Douglas 2022-03-30

Prove the following trig identities:
$2 \sin^{2} θ - 1 = \sin^{2} θ - \cos^{2} θ$
$\cos^{2} t = \sin^{2} t + 2 \cos^{2} t - 1$

ICESSRAIPCELOtblt 2022-03-30

Prove that:
$\sin (45^{\circ}) + \sin (15^{\circ}) = \sin (75^{\circ})$

Beryneingmk39 2022-03-30

Prove that,
${[\sin^{n + 1} (x)]}^{2} + {[\cos^{n + 1} (x)]}^{2} \geq {(\frac{1}{2})}^{n}$ where x is real and n is a non-negative integer.

annlanw09y 2022-03-30

Prove that $f (x) = \cos (\frac{1}{x})$ is not periodic without using calculus

Dominique Pace 2022-03-30

Prove that $\sum_{n \in N} \sin^{3} {\frac{2}{n}}$ converges

blestimd4pz 2022-03-30

Prove that $\sin (z) = \frac{e^{i z} - e^{- i z}}{2 i} = \sin (x) cosh (y) + i \cos (x) sinh (y)$
For complex z=x+iy. How to prove that
$\sin (z) = \frac{e^{i z} - e^{- i z}}{2 i} = \sin (x) cosh (y) + i \cos (x) sinh (y)$
by using the power series definition
$\sin (z) = z - \frac{z^{3}}{3!} + \frac{z^{5}}{5!} - \dots$
and Euler's formula
$e^{z} = e^{x} (\cos (y) + i \sin (y))$ ?

Rolando Wade 2022-03-30

Rearrangement inequality and minimal value of $\frac{\sin^{3} x}{\cos x} + \frac{\cos^{3} x}{\sin x}$
For $x \in (0, \frac{π}{2})$ , is the minimum value of $\frac{\sin^{3} x}{\cos x} + \frac{\cos^{3} x}{\sin x} = 1$ ? So considering $(\frac{1}{\cos x}, \frac{1}{\sin x})$ and $(\sin^{3} x, \cos^{3} x)$ is it right to use the rearrangement inequality and conclude that $\frac{\sin^{3} x}{\cos x} + \frac{\cos^{3} x}{\sin x}$ is more than or equal to $\frac{\sin^{3} x}{\sin x} + \frac{\cos^{3} x}{\cos x}$ which is equal to 1?

David Rodgers 2022-03-30

Rearranging a trigonometric expression
$\tan β = \frac{λ - \cos θ}{\sin θ} \Leftrightarrow \tan β = λ \cdot \csc θ - \cot θ$
Where $λ$ is a constant.
Is it possible to simplify the right hand side term into a single trig function? My goal is to have an equation of the form
$θ = f (β)$
Any help is appreciated.

abitinomaq1 2022-03-30

Prove that $\int_{2017}^{2018} (\arctan (\ln (x)) - \ln (\arctan (x))) d x > 0$

Jaylin Clements 2022-03-30

Prove that $\int_{0}^{\frac{π}{2}} \cos^{m} x \sin^{m} x d x = 2^{- m} \int_{0}^{\frac{π}{2}} \cos^{m} x d x$

Precalculus problems and solutions are hard to find online even though this topic is quite popular among college students majoring in Engineering. Keeping this fact in mind, we decided to provide you with a list of questions and answers that will help you with various precalculus problems. Regardless if it is related to equations or any other problem, these precalculus problems and composite functions examples and solutions below will help you see the logic and compare solutions as you check your original task.

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