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

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

1.	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
Answer» Correct Answer - 9 `sec^(2)u, sec^(4)v, sec^(6)w in [1, oo)` `:. Sec^(2) (u) + sec^(4)(v) + sec^(6) (w) in [3, oo)` `:. Pi (sec^(2) u + sec^(4)v + sec^(6)w) in [3pi, oo)` But `cos^(-1) x + cos^(-1) y + cos^(-1) z in [0, 3pi]` So equation is possible of L.H.S. = R.H.S. `= 3pi` `:. cos^(-1) x = cos^(-1) y = cos^(-1) z = pi` `:. x = y = z =-1` and `sec^(2) u = sec^(4) v = sec^(6) w = 1` `:. u = pi, v = 2pi, w = 3pi` `:. x^(2000) + y^(2002) + z^(2004) + (36pi)/(u + v + w) = 1 + 1 + 1 + (36pi)/(6pi) = 9`

`tan^(-1)[(cosx)/(1+sinx)]`is equal to`pi/4-x/2,forx in (-pi/2,(3pi)/2)``pi/4-x/2,forx in (-pi/2,pi/2)``pi/4-x/2,forx in (-pi/2,pi/2)``pi/4-x/2,forx in (-(3pi)/2,pi/2)`
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Find the principal value of `sin^(-1)(-1/sqrt2)+tan^(-1)(-1/sqrt3)+sec^(-1)(2)`