Question

need help im stuck

i need to prove that

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

Answer 1

i forgot to mention that i have to start on the left side x.x

Answer 2

i original problem is prove:

cos2x = 1 - tan^2x
----------
1+tan^2x

Answer 3

\[(1-\frac{sinx}{cosx}){(1+\frac{sinx}{cosx})}\]\[(1-\frac{\sin^2x}{\cos^2x})\]\[1-\sin^2x \times \frac{1}{\cos^2x}\]\[(1-\sin^2x)(\sec^2x).\]

Answer 4

aaaaaaaaaa lol gotcha xD thank you

Answer 5

yw :)

Answer 6

?

Answer 7

\[(1+\tan(x))(1-\tan(x))\]
\[1-\tan^2(x)\]
\[1-\frac{\sin^2(x)}{\cos^2(x)}\]
He is right until this point.

Answer 8

? ------> ??

Answer 9

hi

Answer 10

Hint 1: Combine the fractions

Answer 11

Hint 2: Rewrite the numerator in terms of sin by using the Pythagorean identity, \[\cos^2(x)=1-\sin^2(x)\]