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The sum of all values of theta in (0,pi/...

The sum of all values of `theta in (0,pi/2)` satisfying `sin^(2)2theta+cos^(4)2theta=3/4` is

A

`pi`

B

`(3pi)/8`

C

`(5pi)/4`

D

`(pi)/2`

Text Solution

Verified by Experts

The correct Answer is:
D
`sin^(2)2theta+cos^(4)2theta=3/4`
Put `sin^(2)2theta=t`
`t+(1-t)^(2)=3/4`
`t+t^(2)+1-2t=3/4`
`t^(2)-t+1/4=0`
`(t-1/2)^(2)=0`
`t=1/2`
`sin^(2)2theta=1/2`
`sin^(2)2theta=pm1/(sqrt2)`
`2theta=(pi)/4,(3pi)/4`
`theta=(pi)/8,(3pi)/8`
`(pi)/8+(3pi)/8=(pi)/2`
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