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Evaluate: sin(1/2cos^(-1)4/5)...

Evaluate: `sin(1/2cos^(-1)4/5)`

A

`1/sqrt(5)`

B

`2/sqrt(5)`

C

`1/sqrt(10)`

D

`2/sqrt(10)`

Text Solution

Verified by Experts

The correct Answer is:
C
Let `cos^(-1)4/5=x`, where `x in [0,pi]`. Then, `cosx=4/5`.
Since, `x in [0,pi] to 1/2 x in [0,pi/2] rArr sin1/2 x gt 0`.
`sin(1/2cos^(-1)4/5) = sin1/2x =sqrt((1-cosx)/2)=sqrt((1-4/5)/(2))=1/sqrt(10)`.
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