If a = (cosθ + i sinθ), prove that .
Given: a = cosθ + isinθ
To prove:
Taking LHS,
Putting the value of a, we get
We know that,
1 + cos2θ = 2cos2θ
or
and
Using the above two formulas
Using,
Rationalizing by multiply and divide by the conjugate of
Putting i2 = -1, we get
We know that,
cos2 θ + sin2 θ = 1
= RHS
Hence Proved