Question

Cos3theta=K(a^3+1/a^3) find value of K

Answer 1

Step-by-step explanation:

Let

a=(cosθ+isinθ)=e

iθ

a

1

=

a

ˉ

=(cosθ−isinθ)=e

−iθ

Hence

a+

a

1

=a+

a

ˉ

=2cosθ ...(i)

Now

a

n

=(cosθ+isinθ)

n

=e

inθ

=cosnθ+isinθ ...(ii)

SImilarly

a

n

1

=

a

ˉ

n

=cosnθ−isinθ ...(iii)

Hence

a

n

+

a

n

1

=2cosnθ

Substituting n=3, we get

a

3

+

a

3

1

=2cos3θ

∴ cos3θ=

2

1

(a

3

+

a

3

1

)

I hope it's help you...