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prove (sin(2x))/(sin(x))-(cos(2x))/(cos(x))=sec(x)

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

☐²

x^☐

√☐

^□√☐

□□

log_□

θ

∞

∫

ddx

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

laplace bernoulli substitution linear exact

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Steps Examples

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characteristic polynomial (

`a`	1
0	2`a`

)

Solution

(−λ+a)(−λ+2a)

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Solution steps

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(

`a`	1
0	2`a`

)

Matrix characteristic polynomial

A characteristic polynomial of square matrix A is defined as det(A−λI) where I is the identity matrix of same dimension as A

(

`a`	1
0	2`a`

)−λ(

1	0
0	1

)=(

`a`−λ	1
0	2`a`−λ

)

=det(

`a`−λ	1
0	2`a`−λ

)

det(

`a`−λ	1
0	2`a`−λ

)=(−λ+a)(−λ+2a)

=(−λ+a)(−λ+2a)

(−λ+a)(−λ+2a) وسٌع: λ²−3aλ+2a²

=λ²−3aλ+2a²

=(−λ+a)(−λ+2a)

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

prove (sin(2x))/(sin(x))-(cos(2x))/(cos(x))=sec(x)

Solution

Solution steps

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