Question

Show(1-tanx)/(1+tanx)^2 = cos2x?

Answer 1

is that cos^2(x) or cos(2x)

Answer 2

cos(2x)

Answer 3

okay start with the trig identiy for cos(2x)

Answer 4

http://prntscr.com/86l5g2 this one

Answer 5

turn tan in sin/cos and play around with it, tell me if u are still stuck

Answer 6

how to settle the(1+tanx)^2
i keep cant not get the answer cos2x

Answer 7

To me, it is not an identity. Counterexample
Let test x = pi/6,
the LHS = 0.1698729811
while the RHS =0.5

Answer 8

can do full step to me?
i realy no idea==

Answer 9

to convert (1-tanx)/(1+tanx)^2 to cos2x

Answer 10

try to simplify (1+tanx)^2 to (sec^2x+2tanx)
sec^2x+2sinx/cosx

Answer 11

do like dan suggested transfer tan to sin/cos
that will be helpful

Answer 12

if it is (1-tan^2x)/(1+tan^2x)^2

Answer 13

?

Answer 14

hmm no i was talking about the denominator of left hand side
(1+tanx)^2

Answer 15

manupilate that a bit more into sin and cos

Answer 16

then after that do the same with top too

Answer 17

but there is the square2 there confusing me

Answer 18

the square you need to distribute
like you do with (a+b)^2

Answer 19

is(1+tan^4x) equal to sec^4x?

Answer 20

no

Answer 21

there is no such identity
we have 1+tan^2x=sec^2x

Answer 22

let me start a bit
\(\huge \frac{1-\tan x}{\sec^2x +2\frac{\sin x}{\cos x}}=\frac{\frac{\cos x-\sin x}{\cos x}}{\frac{1}{\cos^2x}+2\frac{\sin x}{\cos x }}\)

Answer 23

see if you can finish it off

Answer 24

you can cancel that cos that is in top and bottom