If (cosθ+isinθ)(cos2θ+isin2θ)...(cosnθ+isinnθ)=1, then the value of θ is
2mπnn+1
4mπ
4mπnn+1
mπnn+1
Explanation for the correct option:
Find the value of θ:
Given, (cosθ+isinθ)(cos2θ+isin2θ)...(cosnθ+isinnθ)=1
⇒ eiθe2iθe3iθ….einθ=1 ; [Euler's form]
⇒ ei(θ+2θ+3θ+…nθ)=1
⇒ ein(n+1)θ/2=ei2mπ
⇒ n(n+1)θ2=2mπ
∴θ=4mπn(n+1)
Hence, Option ‘C’ is Correct.
Evaluate :cos48°-sin42°