1.

If `sin^ 4 x/2+cos^4 x/3 =1/5` thenA. `tan^(2) x = (2)/(3)`B. `(sin^(8)x)/(8) + (cos^(8)x)/(27) = (1)/(125)`C. `tan^(2)x=(1)/(3)`D. `(sin^(8)x)/(8)+(cos^(8)x)/(27)=(2)/(125)`

Answer» Correct Answer - A::B
`(sin^(4)x)/(2)+(cos^(4)x)/(3)=(1)/(5)implies(sin^(4)x)/(2)+((1-sin^(2)x)^(2))/(3)=(1)/(5)`
`implies(sin^(4)x)/(2)+(1+sin^(4)x-2sin^(2)x)/(3)=(1)/(5)`
`implies 5 sin^(4)x-4sin^(2)x+2=(6)/(5)`
`implies 25sin^(4)x-20sin^(2)x+4=0`
`implies(5sin^(2)x-2)^(2)=0`
`implies sin^(2)x = (2)/(5) cos^(2)x = (3)/(5), tan^(2)x=(2)/(3)`
`therefore" "(sin^(8)x)/(8)+(cos^(8)x)/(27)=(1)/(125)`


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