sin^{-1}(1-x)-2sin^{-1}x=pi/2

Find the principal value of

sin ( 2 sin^{ -1} (2/3))

If y=cot^{-1}(square root cosx) - tan^{-1}(square root cosx)

prove that sin y= tan^{2} x/2.

if tan-1x+tan-1y+tan-1z=π/2 show that xy+yz+zx=1?

Principle value of:

sec-1[cosec pie/8]

Solve for x : sin-1 6x + sin-1 6root3 x = -pi/2

solve for X

sin-1x + sin-12x = ∏/3

Solve for the equation cos (tan^{-1}x) = sin(cot^{-1}3/4)

Domain of f(x) = cos-1x + cot-1x+ cosec-1x is

A [-1,1] B R C (-INFINITY,-1]U[1,INFINITY) D {-1,1}

ANswer is D. EXPLAIN PLEASE!

if sin ^{-1}x +sin^{-1} y+ sin^{-1} z= pie ,prove that

a)x( root 1-x^{2})+y( root 1- y^{2})+ z(root 1-z^{2})= 2xyz

b)x^{4}+ y^{4}+z^{4}+ 4 x^{2}y^{2}z^{2}= 2( x^{2}y^{2}+y^{2}z^{2}+ z^{2}x^{2})

If tan-1{root (1+x^{2}) - root(1-x^{2})}/{ root (1+x^{2}) +root (1-x^{2})} =theta , then prove that x^{2} =sin 2 theta .

Solve the equation:

sin-1 (3x/5) + sin-1(4x/5)= sin-1x

Solve for x - tan^-1 (x+1) + tan^-1 (x-1) = tan^-1 8/31

cos cos^{-1} [-root3/2] +pi/4]

prove that

2tan^{-1} [ { (a-b) / (a+b) }^{1/2 }tan x/2 ] = cos^{-1}{ (b +acos x ) / (a+bcos x) }

prove that sec square (tan inverse 2) +cosec square (cot inverse 3) =15

URGENT !!

sin^{-1}x+sin^{-1}y+sin^{-1}z=π,prove thatx^2 -y^2-z^2 +2yz *square root 1-x^2=0

please answer in a simple and understanding way....

sin

^{-1}(1-x)-2sin^{-1}x=pi/2Find the principal value of

sin ( 2 sin

^{ -1}(2/3))If y=cot

^{-1}(square root cosx) - tan^{-1}(square root cosx)prove that sin y= tan

^{2}x/2.if tan-1x+tan-1y+tan-1z=π/2 show that xy+yz+zx=1?

Principle value of:

sec-1[cosec pie/8]

cos(tan

^{-1}(15/8)-sin^{-1}(7/24))=297/425.Solve for x : sin-1 6x + sin-1 6root3 x = -pi/2

solve for X

sin-1x + sin-12x = ∏/3

Solve for the equation cos (tan

^{-1}x) = sin(cot^{-1}3/4)^{-1}(1-x) - 2 sin^{-1}x =π/2 .^{-1 }(x + 1) ) = cos ( tan^{-1}x ) ...... find x ..... i asked this question and an expert proved it wrong .....but this question is absolutely correct ...it's 2015 board question .... so kindly find x ...since question is correct ..!!! @ PRIYANKA KEDIA ......AND OTHER MERITNATION EXPERTS ....!!!Domain of f(x) = cos-1x + cot-1x+ cosec-1x is

A [-1,1] B R C (-INFINITY,-1]U[1,INFINITY) D {-1,1}

ANswer is D. EXPLAIN PLEASE!

if sin

^{-1}x +sin^{-1}y+ sin^{-1}z= pie ,prove thata)x( root 1-x

^{2})+y( root 1- y^{2})+ z(root 1-z^{2})= 2xyzb)x

^{4}+ y^{4}+z^{4}+ 4 x^{2}y^{2}z^{2}= 2( x^{2}y^{2}+y^{2}z^{2}+ z^{2}x^{2})If tan-1{root (1+x

^{2}) - root(1-x^{2})}/{ root (1+x^{2}) +root (1-x^{2})} =theta , then prove that x^{2}=sin 2 theta .Solve the equation:

sin-1 (3x/5) + sin-1(4x/5)= sin-1x

Solve for x - tan^-1 (x+1) + tan^-1 (x-1) = tan^-1 8/31

cos cos

^{-1}[-root3/2] +pi/4]prove that

2tan

^{-1}[ { (a-b) / (a+b) }^{1/2 }tan x/2 ] = cos^{-1}{ (b +acos x ) / (a+bcos x) }prove that sec square (tan inverse 2) +cosec square (cot inverse 3) =15

URGENT !!

sinx+^{-1}siny+^{-1}sinz=π,prove thatx^2 -y^2-z^2 +2yz *square root 1-x^2=0^{-1}please answer in a simple and understanding way....

pls answer , I have a test tomorrow :/