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prove (2tan(x))/(1+tan^2(x))=sin(2x)

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`x`²	`x`^□	log_□	√☐	^□√☐	≤	≥	□□	·	÷	`x`^◦	π
(☐)^′	`ddx`	∂∂`x`	∫	∫_□^□	lim	∑	∞	`θ`	(`f` ◦ `g`)	`f`(`x`)

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□□

log_□

θ

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∫

ddx

≥	≤	·	÷	`x`^◦	(☐)	\|☐\|	(`f` ◦ `g`)	`f`(`x`)	ln	`e`^☐
(☐)^′	∂∂`x`	∫_□^□	lim	∑	sin	cos	tan	cot	csc	sec

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alternating test ∑_n=1^∞(−1)ⁿ⁺¹neⁿ

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(

4	4	2	3	−2
0	1	−2	−2	2
6	12	11	2	−4
9	20	10	10	−6
15	28	14	5	−3

)

Matrix eigenvectors

Let A be a square matrix, η a vector and λ a scalar that satisfy Aη=λη,
then η is an eigenvector of A and λ is the eigenvalue associated with it

To find the eigenvectors η, solve (A−λ I)η=0 for each eigenvalue λ

Find the eigenvalues for (

4	4	2	3	−2
0	1	−2	−2	2
6	12	11	2	−4
9	20	10	10	−6
15	28	14	5	−3

): λ=3 with multiplicity of 2, λ=5 with multiplicity of 2, λ=7

Eigenvectors for λ=3: (

−3

), (

−2

)

Eigenvectors for λ=5: (

−2

), (

−1

)

Eigenvectors for λ=7: (

)

The eigenvectors for (

4	4	2	3	−2
0	1	−2	−2	2
6	12	11	2	−4
9	20	10	10	−6
15	28	14	5	−3

)

−3

), (

−2

), (

−2

), (

−1

), (

)

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Hi, ask a question about eigenvectors (

4	4	2	3	−2
0	1	−2	−2	2
6	12	11	2	−4
9	20	10	10	−6
15	28	14	5	−3

) or choose below

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−▭▭	<	7	8	9	÷	`AC`
+▭▭	>	4	5	6	×	☐☐☐
×▭▭	(	1	2	3	−	`x`
▭ \|▭	)	.	0	=	+	`y`

prove (2tan(x))/(1+tan^2(x))=sin(2x)

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Solution steps

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