Question

Show that (cos a + isina)^3 = cos 3a +isin3a

Answer 1

Answer:

proved

Step-by-step explanation:

we know that

${e}^{ia} = cosa + isina$

cubing both the sides,

we get,

${e}^{3ia} = {(cosa + isina)}^{3}$

e^3ia=cos3a +i sin3a

proved

Answer 2

Answer with Step-by-step explanation:

LHS

$(cosa+isina)^3$

We know that

$cos\theta+isin\theta=e^{i\theta}$

Using the formula

$(e^{ia})^3$

$e^{i(3a)}$

By using the formula

$(e^{x})^ n}=e^{nx}$

$cos(3a)+isin(3a)$

LHS=RHS

Hence, proved.

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