If `cos^(-1)(x)+cos^(-1)(y)+cos^(-1)(z)=pi(sec^2(u)+sec^4(v)+sec^6(w)),w h e r e u , v , w` are least non-negative angles such that `u

Explanation

`cos^-1x+cos^-2y+cos^-1z = pi(sec^2u+sec^4v+sec^6w)`

Maximum value of `cos^-1x+cos^-2y+cos^-1z` can be `3pi`.

Minimum value of `pi(sec^2u+sec^4v+sec^6w)` can be `3pi`.

`:. cos^-1x+cos^-2y+cos^-1z = pi(sec^2u+sec^4v+sec^6w) = 3pi`

`:. cos^-1x = cos^-2y = cos^-1z = pi`

`=> x = y = z cospi = -1`

Now, `pi(sec^2u+sec^4v+sec^6w) = 3pi`

`=>sec^2u+sec^4v+sec^6w = 3`

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