Home
Class 12
MATHS
If sin^(-1)x+sin^(-1)y+sin^(-1)z=pi, the...

If `sin^(-1)x+sin^(-1)y+sin^(-1)z=pi`, then prove that `x^(4)+y^(4)+z^(4)+4x^(2)y^(2)z^(2)=2(x^(2)y^(2)+y^(2)z^(2)+z^(2)x^(2))`

Promotional Banner

Topper's Solved these Questions

  • SAMPLE PAPER - 19 (UNSOLVED)

    FULL MARKS|Exercise PART - IV (IV. Answer all the questions.)|14 Videos

  • SAMPLE PAPER - 19 (UNSOLVED)

    FULL MARKS|Exercise PART - II (II. Answer any seven questions. Questions No. 30 is compulsory.)|9 Videos

  • SAMPLE PAPER - 18 (UNSOLVED)

    FULL MARKS|Exercise PART - IV (IV. Answer all the questions.)|13 Videos

  • SAMPLE PAPER - 2

    FULL MARKS|Exercise PART -IV (Answer the questions)|11 Videos

Similar Questions

Explore conceptually related problems

IF sin^(-1) X+ sin^(-1) y+ sin^(-1) z= pi , then prove that x^4 +y^4+ z^4 +4x^2 y^2 z^2 = 2(x^2 y^2 +y^2 z^2+z^2x^2).

If sin^(-1)x+sin^(-1)y+sin^(-1)z=pi,t h e nx^4+y^2+z^4+4x^2y^2z^2=K(x^2y^2+y^2z^2+z^2x^2), where K is equal to 1 (b) 2 (c) 4 (d) none of these

If sin^(-1)x+sin^(-1)y+sin^(-1)z=(3pi)/(2) , the value of x^(2017)+y^(2018)+z^(2019)-(9)/(x^(101)+y^(101)+z^(101)) is

Find GCD of 25x^(2) y^(2)z, 45x^(2) y^(4) z^(3) b

If (sin^(-1)x)^2+(sin^(-1)y)^2+(sin^(-1)z)^2=3/4pi^2 , find the value of x^2+y^2+z^2 .

If cos^(-1)x+cos^(-1)y+cos^(-1)z=pi,t h e n (a) x^2+y^2+z^2+x y z=0 (b) x^2+y^2+z^2+2x y z=0 (c) x^2+y^2+z^2+x y z=1 (d) x^2+y^2+z^2+2x y z=1

If cos^(-1) x + cos^(-1) y + cos ^(-1) z = pi and 0 lt x,y,z lt 1 show that x^(2) +y^(2) +z^(2) +2xyz = 1

Show that |(1,1,1),(x,y,z),(x^(2),y^(2),z^(2))|=(x-y)(y-z)(z-x)

If x + y + z = xyz, then prove that (2x)/(1- x^(2)) + (2y)/(1 - y^(2)) + (2z)/(1 - z^(2)) = (2x)/(1 - x^(2))cdot (2y)/(1 - y^(2))cdot (2z)/( 1- z^(2)) .