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Solve sin^2x+cos^2y=2sec^2z for x , y ,a...

Solve `sin^2x+cos^2y=2sec^2z` for `x , y ,a n dzdot`

Text Solution

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`L.H.S. = sin^(2)x+cos^(2) y le 2" "[ :' sin^(2)x le and cos^(2) y le 1]`
`R.H.S.=2 sec^(2) z ge 2`
Hence, `L.H.S.=R.H.S.` only when `sin^(2) x=1`,
`cos^(2) y=1, and 2 sec^(2) z=2`.
Thus, `cos^(2) x=0, sin^(2) y=0, cos^(2) z=1`
`rArr cos x=0, sin y=0, sin z =0`
`x=(2m+1) pi/2, y = n pi`
and `z=tpi`, where `m, n t in Z`.
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