Question

Simplyfy by de moivers theorem (cos6 theta + i sin theta)-³(cos theta + i sin theta)÷(cos2 theta- i sin 2 theta )⁴(cos 3 theta+ i sin 3 theta)-³

Answer 1

Answer:

sinθ+cosθ=x

⇒sin

2

θ+cos

2

θ+2sinθcosθ=x

⇒1+2sinθcosθ=x

⇒sinθcosθ=(x−

2

1

)

sin

6

θ+cos

6

θ=(sin

2

θ)

3

+(cos

2

θ)

3

=(sin

2

θ+cos

2

θ)(sin

4

θ+cos

4

θ−sin

2

θcos

2

θ)

=((sin

2

θ+cos

2

θ)

2

−2sin

2

θcos

2

θ−sin

2

θcos

2

θ)=1−3sin

2

θcos

2

θ

=1−

4

3(x−1)

2

=

4

4−3(x−1)

2

.