Precalculus Solutions | Expert Assistance for Problems & Examples

Prove that $\frac{\sin 5 x}{\sin x} \in (- \frac{5}{4}, 5)$ for any $x \in R k π$ where $k \in Z$ .

tibukooinm 2022-03-31

Prove that $cosh (x) = \sec (θ)$ if $x = \ln (\sec θ + \tan θ)$

Blackettyl2j 2022-03-31

Prove that $\cos x \cdot \cos \sqrt{3} x = 1$ has exactly one solution at x=0

Sage Fry 2022-03-31

Prove that
$\sin (12^{\circ}) \sin (48^{\circ}) \sin (54^{\circ}) = \frac{1}{8}$

encaderpwp 2022-03-31

Prove that
$\sin (\frac{π}{3} + x) = \cos (\frac{π}{6} - x)$

calcolare45pj 2022-03-31

Prove that
$\int_{0}^{π} \frac{\cos x \cos 4 x}{{(2 - \cos x)}^{2}} d x = \frac{π}{9} (2160 - 1247 \sqrt{3})$

Zoie Phillips 2022-03-31

Prove that
$\frac{1}{90} \sum_{n = 1}^{90} 2 n \cdot \sin ({(2 n)}^{\circ}) = \cot (1^{\circ})$

Alfredo Holmes 2022-03-31

Prove that
$\cos^{2} (θ) + \cos^{2} (θ + 120^{\circ}) + \cos^{2} (θ - 120^{\circ}) = \frac{3}{2}$

michiiiiiakqm 2022-03-31

Prove that
$(\sin^{2} \frac{x}{2}) \cdot \frac{\sqrt[3]{4}}{3} \cdot {\frac{1}{\sin x + 1 - x}}^{\frac{2}{3}}} < 1$

Anika Boyd 2022-03-31

Prove $\sin 8 θ - \sin 10 θ = \cot 9 θ (\cos 10 θ - \cos 8 θ)$

Nadia Clayton 2022-03-31

Prove $\frac{\cos (x)}{1 - \tan (x)} + \frac{\sin (x)}{1 - \cot (x)} = \sin (x) + \cos (x)$

aanvarendbq28 2022-03-31

Prove ${[\cos (θ + \frac{π}{3}) + i \sin (θ + \frac{π}{3})]}^{6} = \cos (6 θ) + i \sin (6 θ)$

Pizzadililehz 2022-03-31

Prove $(1 + \sec x) (1 + \csc x) > 5$ if $x \in [0, \frac{π}{2}]$ .

markush35q 2022-03-31

Prove
$\sin (5 θ) = 16 \sin^{5} (θ) - 20 \sin^{3} (θ) + 5 \sin (θ)$

Jasmine Todd 2022-03-31

Proof that
$2 \sin (1.5 x) \cos (1.5 x) = 3 \sin (x) - 4 \sin^{3} (x)$

acidizihvzs 2022-03-31

Proof of trig identity using t-formulae
Show that
$2 \arctan x = \arccos \frac{1 - x^{2}}{1 + x^{2}}$
if x>0, and
$2 \arctan x = - \arccos \frac{1 - x^{2}}{1 + x^{2}}$
if x<0.
I have been able to equate the expressions by letting $x = \tan (\frac{y}{2})$ , but I do not know how to show the different signs of the equation for x>0 and x<0.

David Rodgers 2022-03-31

Proof of $\cos α + \sin β + \cos γ = 4 \cdot \sin (\frac{α}{2} + 45 °) \cdot \sin \frac{β}{2} \cdot \sin (\frac{γ}{2} + 45 °)$
I tried to simplify right side:
$4 (- \frac{1}{2} (\cos (\frac{α}{2} + \frac{γ}{2} + \frac{π}{2}) - \cos (\frac{α}{2} - \frac{γ}{2})) \cdot \sin (\frac{β}{2}) =$
$= - 2 \cdot \sin (β) \cdot \cos (\frac{α}{2} + \frac{γ}{2} + \frac{π}{2}) + 2 \cos (\frac{α}{2} - \frac{γ}{2}) \cdot \sin (\frac{β}{2}) =$
$= - \sin (\frac{β}{2} + \frac{α}{2} + \frac{γ}{2} + \frac{π}{2}) - \sin (\frac{β}{2} - \frac{α}{2} - \frac{γ}{2} - \frac{π}{2}) + \sin (\frac{β}{2} + \frac{α}{2} - \frac{γ}{2}) + \sin (\frac{β}{2} - \frac{α}{2} + \frac{γ}{2})$

ashes86047xhz 2022-03-31

Proof of
$\sum_{n = 1}^{\infty} \frac{1}{n^{3}} \frac{sinh π n \sqrt{2} - \sin π n \sqrt{2}}{cosh π n \sqrt{2} - \cos π n \sqrt{2}} = \frac{π^{3}}{18 \sqrt{2}}$

ruililorNokmncf 2022-03-31

Proof of
$- \ln (2 \sin (\frac{x}{2})) = \sum_{k = 1}^{\infty} \frac{\cos (k x)}{k}$

aanvarendbq28 2022-03-30

I have worked an integral and reduced the integral to
$\frac{n π + \sin (\frac{n π}{2}) - \sin (\frac{3 π n}{2})}{2 n π}$

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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