Question

DE~!

Answer 1

\[y=\tan^{-1} \sqrt{\frac{1-cosx}{1+cosx}} \]

Answer 2

I tried to solve till some extent

Answer 3

well, you might notice that if the part behind there look very very similar to \(\tan \theta\) if you've done some rearranging.

Answer 4

and the answer is \[\large \frac{ dy }{ dx }=\frac{ 1 }{ 2 }\]right?

Answer 5

try to get y=x/2.

Answer 6

\[\frac{dy}{dx}=\frac{1}{1+\frac{1-cosx}{1+cosx}} \times \frac{1}{2 \sqrt{\frac{1+cosx}{1-cosx}}} \times 1+\cos x d(\frac{1-cosx}{(1+cosx)^{2}}) - (1-cosx) d \frac{1+cosx}{(1+cosx) ^{2}} \]

Answer 7

wth :o

Answer 8

use the half angle formulas to reduce \(\sqrt \frac{1- \cos x}{1+\cos x}\) into \(\tan \frac{x}{2}\), then start differentiating.

Answer 9

use
1-cos 2theta =... ?
1-sin 2theta=.....?
in terms of theta.

Answer 10

*1+cos 2theta=...

Answer 11

2cos^2 theta

Answer 12

where do i have to use it but?

Answer 13

so, 1+cos x = 2cos^2 x
right ?

Answer 14

*1+cos x = 2cos^2 (x/2)

Answer 15

yeah! u confused me for a second :P

Answer 16

ans 1-cos x = ?

Answer 17

-2cos(x/2)?

Answer 18

no!

Answer 19

:O

Answer 20

1-cos 2theta = 2 sin^2 theta

Answer 21

yes

Answer 22

so, 1-cos x = ?

Answer 23

2sin sq theta/2

Answer 24

2sin^2 x/2
now put this in your y=...

Answer 25

what u get ?

Answer 26

2cos ^ theta/2sin ^ theta

Answer 27

2 theta on the LHS of the identity, theta on the RHS of the identity
x on the LHS, what do you think is the RHS?

Answer 28

thatis powerr 2*

Answer 29

yeah, and theres square root, so that simplifies to ?

Answer 30

cos/sin

Answer 31

tan theta :o

Answer 32

sin/cos = tan (x/2)

Answer 33

yes

Answer 34

so y=... ?

Answer 35

tan inverse tan x/2

Answer 36

\[\frac{1}{1+\frac{\tan^{2}x}{4}} \]?

Answer 37

\(\tan^{-1}(tan \theta) = \theta\)

Answer 38

tan^{-1} is supposed to "cancel" the tan, basic concept of an inverse function.

Answer 39

\(\tan^{-1}(tan \: x/2) = x/2\)

Answer 40

oh.! okay...thanks :D

Answer 41

Arigato senseis'!

Answer 42

whats that ?

Answer 43

Thank you,teacher(s) <3

Answer 44

japanese phrase :P

Answer 45

ohh! welcome ^_^

Answer 46

sensei = teacher hahaha

Answer 47

yeah ! :D