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The simplified form of sqrt(1+sin""((x)/...

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

A

`sin""((x)/(8))+cos""((x)/(8))`

B

`sin""((x)/(16))+cos""((x)/(16))`

C

`sin""((x)/(4))+cos""((x)/(4))`

D

None of these

Text Solution

Verified by Experts

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