Prove the identity (1-tan^2x)/(1+tan^2x) is same as 1-2sin^2x?

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Prove the identity (1-tan^2x)/(1+tan^2x) is same as 1-2sin^2x?

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Answer 1 · 2017-11-14T19:51:39

See below.

Explanation:

Using Identities:

$color(red)(tan^2x=sin^2x/cos^2x)$

$color(red)(sin^2x+cos^2x=1)$
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$LHS$

$(1-(sin^2x)/cos^2x)/(1+sin^2x/cos^2x)$

Multiply by $cos^2x$ :

$(cos^2x-sin^2x)/(cos^2x+sin^2x)$

$color(red)(sin^2x+cos^2x=1)$

$cos^2x-sin^2xcolor(white)(88)$ ( $cos^2x= 1-sin^2x$ )

$1-sin^2x-sin^2x$

$1-2sin^2x$

$LHS -=RHS$

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Prove the identity (1-tan^2x)/(1+tan^2x) is same as 1-2sin^2x?

1 Answer

Explanation:

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