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If sin2theta=cos3theta and theta is an a...

If `sin2theta=cos3theta` and `theta` is an acute angle , then `sintheta` is equal to

A

`(sqrt(5)-1)/(4)`

B

`-((sqrt(5)-1)/(4))`

C

`(sqrt(5)+1)/(4)`

D

`(-sqrt(5)-1)/(4)`

Text Solution

Verified by Experts

The correct Answer is:
A
`sin 2 theta=cos 3theta`
or `2 sin theta cos theta=4cos^(3)theta-cos theta`
or `2sin theta=4(1-sin^(2)theta)-3`
or `4sin^(2)theta+2sin theta-1=0`
or `sin theta=(sqrt(5)-1)/(4)`
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