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If sin2theta=cos3theta, "where"0ltthetal...

If `sin2theta=cos3theta, "where"0ltthetalt(pi)/(2)`, then what is sin `theta` equal to ?

A

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

B

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

C

`(sqrt(5)+1)/(16)`

D

`(sqrt(5)-1)/(16)`

Text Solution

Verified by Experts

The correct Answer is:
B
`sin2theta=cos3theta`
`rArrsin2theta=sin(90^(@)-3theta)`
`2theta=90^(@)-3theta" " thereforesintheta=sin18^(@)=(sqrt(5)-1)/(4)`
`rArr5theta=90^(@)`
`rArrtheta=18^(@)`
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