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If sin^ 4 x/2+cos^4 x/3 =1/5 then...

If `sin^ 4 x/2+cos^4 x/3 =1/5` then

A

`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)`

Text Solution

Verified by Experts

The correct Answer is:
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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