Home
Class 12
MATHS
Solve the following equations: si...

Solve the following equations: `sin[2cos^(-1)"{"cot"("2tan^(-1)x"}]"=0`

A

`pm1`

B

`1pm sqrt(2)`

C

`-1pm sqrt(2)`

D

`pm sqrt(2)`

Text Solution

Verified by Experts

The correct Answer is:
A, B, C
`because sin[2 cos^(-1){cot^(-1){cot(2 tan^(-1)x)}]=0`
`rArr 2 cos^(-1){cot(2 tan^(-1)x)}=n pi, n in I`
`rArr cos^(-1)(cot(2 tan^(-1)x))=(n pi)/(2)`
`rArr cos^(-1)(cot(2 tan^(-1)x))=0, (pi)/(2), pi`
`(because 0 le cos^(-1)x le pi)`
`rArr cot {tan^(-1)((2x)/(1-x^(2)))}=1,0,-1`
`rArr cot{cot^(-1)((1-x^(2))/(2x))}=1,0,-1`
`rArr (1-x^(2))/(2x)=1,0,-1`
`rArr 1-x^(2)=2x,0,-2x`
`rArr x^(2)+2x-1=0, x^(2)-1=0,x^(2)-2x-1=0`
`rArr x=-1 pm sqrt(2), x= pm 1, x=1 pm sqrt(2)`
Promotional Banner

Similar Questions

Explore conceptually related problems

Solve: sin[2\ cos^(-1){cot(2\ tan^(-1)x)}]=0

Solve the following equations : cos (sin^(-1) x) = 1/2

If sin[2cos^(-1){cot(2tan^(-1)x)}]=0,x>0 then x =

Solve sin [2 cos^(-1) { cot (2 tan^(-1) x)}]= 0

If A=sin[cot^(-1){cos(tan^(-1)x)}], then

sin{cot^(-1)[cos(tan^(-1)x)]}=....

Solve the following equation: 2sin^(2)x+sqrt(3)cos x+1=0

Solve the following equations : cos (tan^(-1) x ) = sin (cot^(-1). 3/4)