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Question

Mathematics Question on Trigonometric Identities

If a=cos2α+isin2α and b=cos2β+isin2β then _______

A

ab=cos(α+β)−isin(α+β)\sqrt{ab}=cos(\alpha+\beta)-isin(\alpha+\beta)

B

ab=cos(α+β)+isin(α+β)\sqrt{ab}=cos(\alpha+\beta)+isin(\alpha+\beta)

C

ab=sin(α+β)+icos(α+β)\sqrt{ab}=sin(\alpha+\beta)+icos(\alpha+\beta)

D

ab=sin(α+β)−icos(α+β)\sqrt{ab}=sin(\alpha+\beta)-icos(\alpha+\beta)

Answer

ab=cos(α+β)+isin(α+β)\sqrt{ab}=cos(\alpha+\beta)+isin(\alpha+\beta)

Explanation

Solution

The correct answer is(B): ab=cos(α+β)+isin(α+β)\sqrt{ab}=cos(\alpha+\beta)+isin(\alpha+\beta)