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If sin2 theta=3/4, then sin^(3)theta+cos...

If `sin2 theta=3/4, then sin^(3)theta+cos^(3)theta=`

A

`(sqrt5)/(8)`

B

`(sqrt7)/(8)`

C

`(sqrt11)/(8)`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
D
We have,
`sin^(3)theta+cos^(3)theta=(sintheta+cos theta)(1-(sin2 theta)/(2))`
`=sqrt(1+sin2 theta)(1-(sin2 theta)/(2))`
`=sqrt(1+(3)/(4))(1-(3)/(8))=(sqrt7)/(2)xx5/8=(5sqrt7)/(16)`
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