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If (sin^4x)/2+(cos^4x)/3=1/5t h e n (a...

If `(sin^4x)/2+(cos^4x)/3=1/5t h e n` (a) `tan^2x=2/3` (b) `(sin^8x)/8+(cos^8x)/(27)=1/(125)` (c)`tan^2x=1/3` (d) `(sin^8x)/8+(cos^8x)/(27)=2/(125)`

A

`tan^2x=2/3`

B

`sin^8x/8+cos^8x/27=1/125`

C

`tan^2x=1/3`

D

`sin^8/8+cos^8x/27=2/125`

Text Solution

Verified by Experts

The correct Answer is:
A, B
`sin^4x/2+cos^4x/3=1/5`
`3sin^4x+2(1-sin^2x)^2=6/5`
`rArr 25sin^4x-20 sin^2 x+4=0`
`rArr sin^2x=2/5`
`:. cos^2x=3/5`
`:. tan^2x=2/3`
`and sin^8x/8+cos^8x/27=1/125`
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