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1)

If   a=cos2α+isin2α,b=cos2β+isin2β,c=cos2γ+isin2γ   and   d=cos2δ+isin2δ

 then

abcd+1abcd=


A) 2cos(α+β+γ+δ)

B) 2cos(α+β+γ+δ)

C) cos(α+β+γ+δ)

D) none of these

Answer:

Option B

Explanation:

 we have,

abcd=cos(2α+2β+2γ+2δ)+isin(2α+2β+2γ+2δ)

abcd=cos(α+β+γ+δ)+isin(α+β+γ+δ)  ..(i)

   1abcd=cos(α+β+γ+δ)isin(α+β+γ+δ)   ....(ii)

Adding (i) and (ii) , we obtain

abcd+1abcd=2cos(α+β+γ+δ)