Question

prove that cos 2x = (1 - tan²x) / (1 + tan²x)

Answer 1

hey rushi I hope my ans is correct
plz reply me

Answer 2

Hey !!!

1st method

°•° cos2x = cos²x - sin²x

cos2x = cos²x - sin²x / 1

cos2x = cos²x - sin²x / cos²x + sin²x

[•°• cos²x + sin²x = 1 ]

divided by cos²x on numerator and denominator

we get

cos²x- sin²x /cos²x
---------------------------
cos²x + sin²x / cos²x

=> (1 - tan²x) / (1 + tan²x ) Rhs prooved
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2nd method

cos2x = cos²x - sin²x

cos2x = cos²x - sin²x×cos²x/cos²x ( we can write )

cos²x ( 1 - sin²x/cos²x)

cos²x ( cos²x - sin²x /cos²x)

cos²x ( 1 - tan²x )

( 1 - tan²x)/sec²x

(1 - tan²x )/(1 + tan²x ) Rhs prooved

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Hope it helps you !!! .

@Rajukumar111