Question

(sintheta+icostheta)^4 is equal to​

Answer 1

Step-by-step explanation:

(cosθ+isinθ)

4

=

i

5

(cosθ−isinθ)

5

(cosθ+isinθ)

4

[∵i

2

=−1)

=

i(cosθ−isinθ)

5

(cosθ+isinθ)

4

=−i(cosθ+isinθ)

4

×(

cosθ−isinθ

1

)

5

=−i(cosθ+isinθ)

4

×(cosθ+isinθ)

5

(∵

cosθ+isinθ

1

=cosθ−isinθ)

=−i(cosθ+isinθ)

9

=−i(cos9θ+isin9θ) (∵(cosθ+isinθ)

m

=cosmθ+isinmθ)

=−icos9θ+sin9θ

∴

(sinθ+icosθ)

5

(cosθ+isinθ)

4

=sin9θ−icos9θ