Precalculus Solutions | Expert Assistance for Problems & Examples

How to solve : $\arcsin x - \arcsin (\frac{x}{2}) = \arcsin (\frac{x \sqrt{3}}{2})$
Why can't I figure this one out?? Is it possible to cancel out the arcsins? I know from graphing on my calculator that the answers are -1,0, and 1, but want help getting there by hand.

Polchinio3es 2022-03-31

$\int_{x}^{1} \frac{d t}{1 + t^{2}} = \int_{1}^{\frac{1}{x}} \frac{d t}{1 + t^{2}}$
I showed that
$\int_{x}^{1} \frac{d t}{1 + t^{2}} - \int_{1}^{\frac{1}{x}} \frac{d t}{1 + t^{2}} = \frac{π}{4} - \arctan (x) - [\arctan (\frac{1}{x}) - \frac{π}{4}]$
Since $\arctan (x) + \arctan (\frac{1}{x}) = \frac{π}{2}$ , then it follows that $\int_{x}^{1} \frac{d t}{1 + t^{2}} - \int_{1}^{\frac{1}{x}} \frac{d t}{1 + t^{2}} = 0$ . However, I feel this is kind of proof only "shows" but doesn't really "explains".
Is there another way to prove this? The simpler the better!

mwombenizhjb 2022-03-31

How to solve
$\frac{1}{\sin x} + \frac{\sqrt{3}}{\cos x} = 4$

Nathen Peterson 2022-03-31

How to solve
$\frac{2 \tan x}{1 - {(\tan x)}^{2}} = {(\sin 2 x)}^{2}$

Lucian Ayers 2022-03-31

How to solve
$\sec^{2} x + 3 \csc^{2} x = 8$

Nathen Peterson 2022-03-31

$\cot^{2} \frac{π}{2 m + 1} + \cot^{2} \frac{2 π}{2 m + 1} + \dots + \cot^{2} \frac{m π}{2 m + 1} = \frac{m (2 m - 1)}{3}$
m is a positive integer.

jisu61hbke 2022-03-31

$\frac{1}{{\sin 8}^{\circ}} + \frac{1}{{\sin 16}^{\circ}} + \dots + \frac{1}{{\sin 4090}^{\circ}} + \frac{1}{{\sin 8192}^{\circ}} = \frac{1}{\sin α}$ , find $α$

burubukuamaw 2022-03-31

Proving the identity:
$\sin 3 x + \sin x = 2 \sin 2 x \cos x$

afasiask7xg 2022-03-31

Prove, that
$\sin x - a^{3} \cos x \leq \frac{1}{3} \sqrt{1 + a^{6}}$

Jazmyn Holden 2022-03-31

Prove:
$\frac{1 - \cos 2 θ}{1 - \cos θ} = 2 \cos θ - 2$

Deegan Chase 2022-03-31

Prove the Identity - Double Angle
$\cot (A) = \frac{\sin (2 A)}{1 - \cos (2 A)}$

Nathanael Hansen 2022-03-31

Prove the trigonometric identity:
$\frac{(\cos^{3} x - \sin^{3} x)}{(\cos x - \sin x)} = \frac{(2 + \sin 2 x)}{2}$

Pablo Dennis 2022-03-31

Prove this
$\sin (495^{\circ}) - \sin (795^{\circ}) + \sin (1095^{\circ}) = 0$

blestimd4pz 2022-03-31

Prove the equality
$\tan (π + \frac{x}{3}) > 0$

xxgetthisar08 2022-03-31

Prove the following
$\sin^{4} x + \cos^{15} x = 1$

Rex Maxwell 2022-03-31

Say I want to solve this
$α = 2 \tan^{- 1} (\sqrt{3 - 2 \sqrt{2}})$

Hanzikoval1pa 2022-03-31

Prove that there exists only one number $x \in R$ such that $\sin (x) = x - 1$

Dominique Pace 2022-03-31

Prove that $\sin \frac{π}{14}$ is a root of $8 x^{3} - 4 x^{2} - 4 x + 1 = 0$

palmantkf4u 2022-03-31

Rewrite $f (x) = 3 \sin (π x) + 3 \sqrt{3} + 3 \sqrt{3} \cos (π x)$ in the form $f (x) = A \sin (K x + D)$

Averie Ferguson 2022-03-31

prove that maximum value of $\cos α \cos β$ occurs when $α = β = \frac{σ}{2}$
If $α, β \in (0, \frac{π}{2})$ and $α + β = σ$ (constant), then prove that maximum value of $\cos α \cos β$ occurs when $α = β = \frac{σ}{2}$

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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