Question

If cos theta = 1/2 ( a + 1/ a ) prove that 2 cos 4 theta= a4 +1/a4

Answer 1

Step-by-step explanation:

A^6+a^4+a^2+1=a^4(a^2+1)+1 (a^2+1)

= (a^2+1)(a^4+1).... (eq 1)

here,

a=(1+i)/root 2

or root2*a=1+i

squatting both sides

2a^2=(1+i)^2

or 2a^2=1+2i+i^2

or 2a^2=1+2i+(-1) since i^2=(-1)

a^2=i

or a^4=i^2=(-1)

so from eq (1) ....

a^6+a^4+a^2+1 =(a^2+1)(a^4+1)= (i+1)(-1+1)= 0*(i+1)=0

Answer 2

Step-by-step explanation:

Attachment ✔️✔️

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