Find sin x/2 if cosx =24/25 in first quadrant

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We have given

`cos(x)=24/25`

`cos(x)=1-2sin^2(x/2)`   ,

it is an identity `cos(2theta)=1-2sin^2(theta)`

Thus

`24/25=1-2sin^2(x/2)`

`2sin^2(x/2)=1-24/25`

`2sin^2(x/2)=1/25`

`sin^2(x/2)=1/50`

`sin(x/2)=sqrt(1/50)`   ,

Since x is in first quadrant ,so x/2 also in first quadrant. In first quadrant all trigonometric ratios are positive.

`sin(x/2)=sqrt(2)/10`

Ans.

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