Rewrite the given pair of functions as one composite form

Evalute the composite function at 1.

Josalynn
2021-02-26
Answered

Rewrite the given pair of functions as one composite form

Evalute the composite function at 1.

You can still ask an expert for help

cyhuddwyr9

Answered 2021-02-27
Author has **90** answers

Rewrite the given pair as one composite function as follows.

$g\left(x\left(w\right)\right)=g\left(2{e}^{w}\right)=\sqrt{5\cdot {\left(2{e}^{2}\right)}^{2}}$

Evaluate the above composite function at 1

$g\left(x\left(1\right)\right)=\sqrt{5{\left(2{e}^{1}\right)}^{2}}=\sqrt{5{\left(2e\right)}^{2}}=\sqrt{5\cdot 4\cdot {e}^{2}}=2\sqrt{5}e\approx 12.16$

Evaluate the above composite function at 1

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How to simplify the trigonometric term?

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Why is $\frac{0.5}{{\mathrm{cos}}^{2}\left(30\right)}=\frac{\mathrm{tan}\left(30\right)}{\mathrm{cos}\left(30\right)}$ , but $\frac{0.5}{{\mathrm{cos}}^{2}\left(13\right)}\ne \frac{\mathrm{tan}\left(13\right)}{\mathrm{cos}\left(13\right)}$ ?

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Choose $y\in \mathbb{R}$ so that $\mathrm{sin}y=\frac{u}{\sqrt{{u}^{2}+{v}^{2}}}$ and $\mathrm{cos}y=\frac{v}{\sqrt{{u}^{2}+{v}^{2}}}$

I know the identity${\mathrm{sin}}^{2}y+{\mathrm{cos}}^{2}y=1$ . Also, I notice that

${\left(\frac{u}{\sqrt{{u}^{2}+{v}^{2}}}\right)}^{2}+{\left(\frac{v}{\sqrt{{u}^{2}+{v}^{2}}}\right)}^{2}=1$

without u,v vanishing simultaneously. But I am not sure whether$\mathrm{\exists}y\in \mathbb{R}$ s.t. $\mathrm{sin}y=\frac{u}{\sqrt{{u}^{2}+{v}^{2}}}$ and $\mathrm{cos}y=\frac{v}{\sqrt{{u}^{2}+{v}^{2}}}$ .Does anyone have an idea?

I know the identity

without u,v vanishing simultaneously. But I am not sure whether

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I'm trying to prove the following problem:

$\frac{{\mathrm{sec}}^{2}\left(x\right)}{\mathrm{cot}\left(x\right)}-{\mathrm{tan}}^{3}\left(x\right)=\mathrm{tan}\left(x\right)$

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Given $x=\frac{2\pi}{1999}$

Find the value of

$\mathrm{cos}x\mathrm{cos}2x\mathrm{cos}3x\dots \mathrm{cos}999x$

Find the value of