Question

Guys how would i prove this
(cot(x-1))/(cot(x+1)) = (cos2x)/(1+sin2x)

Answer 1

Theta and x are same

Answer 2

can u coorect ur question ...

Answer 3

?

Answer 4

cos2x= (cosx)^2 - (sinx)^2 =(cosx+sinx)(cosx-sinx)

and 1+sin2x= (cosx)^2 + (sinx)^2 +2sinxcosx=(cosx+sinx)^2


hence RHS = (cos2x)/(1+sin2x) =((cosx)^2 - (sinx)^2 ) / ( (cosx)^2 + (sinx)^2 +2sinxcosx )
= (cosx+sinx)(cosx-sinx)/(cosx+sinx)^2
= (cosx-sinx)/(cosx+sinx)
=((cosx-sinx)/sinx) / ((cosx+sinx)/sinx) [dividing both num and denom by sinx)
=(cosx/sinx - sinx/sinx) / (cosx/sinx + sinx/sinx)

=(cotx -1)/(cotx+1)

Answer 5

so ur LHS hopefully is =(cotx -1)/(cotx+1)

to prove form LHS to RHS
ujust rewrite the above in reverse way

Answer 6

Oh wow thanks ya i miswrote the original problem. If you don't mind me asking, how exactly did u see that i had miswrote it?

Answer 7

u r learning compound angles i suppose..

Answer 8

haha yea. What exactly is the first thing you did to the bottom?

Answer 9

nvm i see what you did

Answer 10

didn't get u..

Answer 11

Hey Thank You so much

Answer 12

welcome