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

The sum of all values of ` theta in (0 , pi)` satisfying ` sin^(2) 2 theta + cos^(4) 2 theta = 1` is:

A

`pi`

B

`(3pi)/(2)`

C

`(5pi)/(2)`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
B
`cos^(4 ) 2 theta = cos^(2 ) 2 theta ) = 0`

` theta in (0, pi) `
`theta = pi/4 , pi/2 , 3pi/4 " " therefore " Sum" = pi/4 + pi/2 + (3pi)/(4) = (6pi)/(4) = (3pi)/(2)`
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