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provar (1-sin(x))/(1+sin(x))=(sec(x)-tan(x))^2

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

Solution

True

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Solution steps

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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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+▭▭	>	4	5	6	×	☐☐☐
×▭▭	(	1	2	3	−	`x`
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provar (1-sin(x))/(1+sin(x))=(sec(x)-tan(x))^2

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