Question

cos(x-y) + cos(y-z)+ cos(z-x) = -3/2 then Σ(cosx) =
​

Answer 1

Answer:

x=1+cos

2

θ+cos

4

θ+...∞

Hence sum of G.P is

=

1−cos

2

θ

1

=

sin

2

θ

1

y=1+sin

2

θ+sin

4

θ+...∞

Hence sum of G.P is

=

1−sin

2

θ

1

=

cos

2

θ

1

z=1+cos

2

θ.sin

2

θ+cos

4

θ.sin

4

θ...∞

=

1−cos

2

θ.sin

2

θ

1

Hence x.y.z

=

cos

2

θ.sin

2

θ

1

.

1−cos

2

θ.sin

2

θ

1

=

cos

2

θ.sin

2

θ(1−cos

2

θ.sin

2

θ)

1

=

cos

2

θ.sin

2

θ(1−cos

2

θ.sin

2

θ)

1−cos

2

θ.sin

2

θ+cos

2

θ.sin

2

θ

=

cos

2

θ.sin

2

θ

1

+

1−cos

2

θ.sin

2

θ

1

=

cos

2

θ.sin

2

θ

cos

2

θ+sin

2

θ

+

1−cos

2

θ.sin

2

θ

1

=

cos

2

θ

1

+

sin

2

θ

1

+

1−cos

2

θ.sin

2

θ

1

=x+y+z

Step-by-step explanation:

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