Question

arccosx=arctanx
prove sin(arccosx)=x^2

Answer 1

m ans is comin x/sqrt1+x^2

Answer 2

thts the condition for the second statement

Answer 3

ya

Answer 4

theres no real soln for the first statemnt

Answer 5

got it

Answer 6

there is actually

Answer 7

see arccosx = arcsin(root(1-x^2))

Answer 8

always....but in ur case its equal to x^2....so root(1-x^2) = x^2

Answer 9

thts the first condition

Answer 10

hain na?

Answer 11

den shal v conlude quest is wrng

Answer 12

if u open the first statement up u get....x^4 + x^2 - 1=0
which is equivalent to x^4 = 1 - x^2

Answer 13

so proved....

Answer 14

m nt getin :(

Answer 15

dekho yaar..suno dhyan se

Answer 16

kaise sunu

Answer 17

\[\sin^{-1}\sqrt{1-x ^{2}} = \cos^{-1}x\]
and
the second statement says that
\[\cos^{-1} x = \sin^{-1}x ^{2}\]
so equating the two statements u can say that
\[x ^{2}= \sqrt{1-x^{2}}\]

Answer 18

him...i think the second equation to prove...how can u start with this?

Answer 19

No looking at ur first statement
\[\cos^{-1} x=\tan^{-1} x\]

which means
\[x =1 /\sqrt{1 + x^{2}}\]
or
\[x^{4} + x^{2} = 1\]

Answer 20

this the second equation says

Answer 21

i think smthin is wrng bcz its nt posible

Answer 22

ab kya hua yaar?

Answer 23

no no him is right...

Answer 24

jai dipankar baba ki...lol:)

Answer 25

u conti

Answer 26

Set \(\cos^{-1}x=\tan^{-1}x=\theta\), then draw a triangle that satisfies the given conditions. A triangle is attached. From the triangle you can easily see that \(\sin(\cos^{-1}x)=\sin\theta=x^2\).

Answer 27

so let me to do a few steps..
him got x^4=1-x^2 from first step...

sin (arccosx)=sin (arcsinsqrt(1-x^2))=sin(arcsinsqrt(x^4))=sin(arcsin x^2)=x^2
this proves ur question...

Answer 28

yes..now u got it?

Answer 29

samajh ayi baat?

Answer 30

ya agai

Answer 31

Are you guys writing in Hindi? :D

Answer 32

yes

Answer 33

nice to be homolingual in a big large world:)

Answer 34

Anwar..dou know hindi?

Answer 35

NO :(

Answer 36

so ui know the term hindi...

Answer 37

Yeah of course.

Answer 38

Anwar come in chat box..