simplify [{(-6^7)^8*(21/1)/(22/1)}^7]^9

Topic

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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

simplify solve for expand factor rationalize

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prove 1−sin(x)1+sin(x) =(sec(x)−tan(x))²

Solution

True

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Solution steps

One step at a time

1−sin(x)1+sin(x) =(sec(x)−tan(x))²

Manipulating right side

(sec(x)−tan(x))²

Express with sin, cos

=(1−sin(x))²cos²(x)

Rewrite using trig identities

=1−sin(x)sin(x)+1

=1−sin(x)1+sin(x)

We showed that the two sides could take the same form

⇒ True

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