prove (cos(x))/(1+sin(x))+(1+sin(x))/(cos(x))=2sec(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

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prove cos(x)1+sin(x) +1+sin(x)cos(x) =2sec(x)

Solution

True

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Solution steps

One step at a time

cos(x)1+sin(x) +1+sin(x)cos(x) =2sec(x)

Manipulating left side

cos(x)1+sin(x) +1+sin(x)cos(x)

Simplify 1+sin(x)cos(x) +cos(x)1+sin(x) : (1+sin(x))²+cos²(x)cos(x)(sin(x)+1)

=(1+sin(x))²+cos²(x)(1+sin(x))cos(x)

Rewrite using trig identities

=2cos(x)

Rewrite using trig identities

2sec(x)

We showed that the two sides could take the same form

⇒ True

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

prove (cos(x))/(1+sin(x))+(1+sin(x))/(cos(x))=2sec(x)

Solution

Solution steps

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