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प्रश्न
If sin θ = 1, then the value of `1/2 sin(theta/2)`is ______.
विकल्प
`1/(2sqrt(2))`
`1/sqrt(2)`
`1/2`
0
उत्तर
If sin θ = 1, then the value of `1/2 sin(theta/2)`is `bbunderline(1/(2sqrt(2)))`.
Explanation:
`sin(theta/2)=+-sqrt((1-costheta)/2)`
`=+-sqrt((1-0)/2)=+-1/sqrt(2)`
Since we are interested in the positive square root (as the principal value for θ = `pi/2` will result in a positive sine value for `theta/2`, we have
`sin(theta/2)=1/sqrt(2)`
Therefore, the value of `1/2 sin (theta/2)`is
`=1/2xx1/sqrt(2)=1/(2sqrt(2))`
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