1.

There exists a value of `theta`between 0 and `2pi`that satisfies the equation `sin^4theta-2sin^2theta-1=0`

Answer» `sin^4theta-2sin^2theta-1=0`
Let `sin^2theta=y`
`y^2-2y-1=0`
`y=(-(-2)pmsqrt(4-4(1)(-1)))/2`
`y=(2pmsqrt8)/2`
`y=(2pm2sqrt2)/2`
`sin^2theta=1pmsqrt2`
`sin^2theta=1+sqrt2`
`sin^2theta=1+1.414`
`sin^2theta=2.414`
`sintheta=pmsqrt2.414`
`sintheta=pm1.55`
There is no value of `theta`.


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