Precalculus Solutions | Expert Assistance for Problems & Examples

Proving $\frac{\cot θ - \csc θ + 1}{\cot θ + \csc θ - 1} = \csc θ - \cot θ$

Rylan Duncan 2022-01-24

Finding the infinite sum involving $\coth$ function using contour integration
I am looking to show: $\sum_{n = 1}^{\infty} \frac{\coth (n π)}{n^{3}} = \frac{7 π^{3}}{180}$

Kaydence Huff 2022-01-24

Different ways gives different results - solving $\tan 2 a = \sqrt{3}$
Case 1)
$\tan 2 a = \sqrt{3} = \tan (\frac{π}{3})$
$2 a = n π + \frac{π}{3}$
$a = \frac{n π}{2} + \frac{π}{6}, n \in Z$
Case 2)
$\frac{2 \tan a}{1 - \tan^{2} a} = \sqrt{3}$
Solving above equation gives $\tan a = \frac{1}{\sqrt{3}} or - \sqrt{3}$
Thus either
$a = n π + \frac{π}{6}, n \in Z$
Or
$a = m π - \frac{π}{3}, m \in Z$
Or either I did something wrong or both these results are same.

Alvin Pugh 2022-01-24

Show $\int_{0}^{2 π} \cos^{2} t d t = π$ using Pythagorean Theorem
The traditional way I always see this integral calculated is with the identity
$\cos^{2} t = \frac{1 + \cos (2 t)}{2}$
My alternative method uses $\cos^{2} t + \sin^{2} t = 1$ . Its

Seamus Kent 2022-01-24

Proving $\frac{1 + \csc^{2} A \tan^{2} C}{1 + \csc^{2} B \tan^{2} C} = \frac{1 + \cot^{2} A \sin^{2} C}{1 + \cot^{2} B \sin^{2} C}$

treetopssan 2022-01-24

Prove angle addition holds for $R^{n}$
Define $θ (u, v) = \cos^{- 1} (\frac{u \cdot v}{| u | | v |})$ be the angle between $u, v \in R^{n}$ , where $u \cdot v$ is the standard inner product and $| x | = \sqrt{x \cdot x}$ for all $x \in R^{n}$ . Let w=su+tv where $s, t \geq 0$ are scalars. Show $θ (u, v) = θ (u, w) + θ (v, w)$ for $u, v \neq 0$

Vilharjevw7 2022-01-24

Simplifying $\sin^{2} (α) \cos^{2} (α)$

framtalshg 2022-01-24

Elementary proof of Bhaskara Is

Jamya Elliott 2022-01-24

How to solve $\cos (\sin^{- 1} (- \frac{3}{5}))$ ?
I tried solving it using the formula $\sin^{2} x + \cos^{2} x = 1$ and I also got $\frac{45}{}$ as the answer but I got it by inputting the value of cosx in the given question in place of
$\sin^{- 1} (- \frac{3}{5})$
But I cant see any logic there.

Seamus Kent 2022-01-24

value of $2 \tan^{- 1} (\csc α) + \tan^{- 1} (2 \sin α \sec^{2} α)$

meteraiqn 2022-01-24

How do you find the compositions given $f (x) = x^{3} + 2$ and $g (x) = \sqrt[3]{x - 2}$ ?

jelentetvq 2022-01-24

Using the general solution for solve $\sin x = \sin y$
We know that $\sin x = \sin y$ implies that $x = 2 k π + y or x = 2 k π + π - y$ . If we want to solve $\sin x = \sin x$ using this method, it gives $x = 2 k π + x or x = 2 k π + π - x$ but it's obvious that solution is $x \in R$ . Why this happens? There is a similar problem for cosx=cosx.

tripplek7i 2022-01-24

Double angle formula equation $\sin (2 x) \cos (2 x) = \frac{1}{4}$

treetopssan 2022-01-24

If $\sin θ - \cos θ \leq μ (\cos θ + \sin θ)$ , then $\tan θ \leq \frac{1 + μ}{1 - μ}$

Carly Shannon 2022-01-24

Why is this true? $\int \frac{d u}{\tan u \cos^{2} u} = \int \frac{d (\tan u)}{\tan u}$

Jamya Elliott 2022-01-24

Solve $\tan x = {\sec 42}^{\circ} + \sqrt{3}$

Natasha Henry 2022-01-24

Given $lim_{x \to 0} \frac{\sin (x)}{x} = 1$ , Prove $lim_{x \to 0} \frac{\sin (x)}{\sin (m x)} = \frac{1}{m}$ for m>0

Anika Osborne 2022-01-24

Prove that $\tan \frac{π}{9} + 4 \sin \frac{π}{9} = \sqrt{3}$

joygielymmeloiy 2022-01-24

Solving $2 \sin (x + 30^{\circ}) = \cos (x + 150^{\circ})$ for x between $0^{\circ} and 360^{\circ}$

Shamar Padilla 2022-01-24

How $\cos^{2} (2 x))^{2} = \frac{1}{4} {(1 + \cos (4 x))}^{2}$
Can you please give me the proof for $\cos^{2} (2 x))^{2} = {\frac{14}{1 + \cos (4 x)}}^{2}$
I know that $\frac{12}{\cos (2 x) + 1} = \cos^{2} x$

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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