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The simplified form of sqrt(1+sin""((x)/(8))) is ______

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Answer Text

`sin""((x)/(8))+cos""((x)/(8))` `sin""((x)/(16))+cos""((x)/(16))` `sin""((x)/(4))+cos""((x)/(4))` None of these

Answer :
B
Solution :
(i) Apply `sqrt(1+sin2A)= sinA+ cos A`. <br> (ii) `sin""(x)/(8) = sin2((x)/(16)) and sin2 theta=2 sin theta cos theta. ` <br> (iii) Use the identity `1=sin^(2) theta + cos^(2) theta`.

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