Question

Solve 6g hahahahshhshhshhshs

Answer 1

Answer:

6g) We proved the equality $cos4A=8cos^{4}A-8cos^{2}A+1$ is true and hence proved.

Step-by-step explanation:

Given equation is $cos4A=8cos^{4}A-8cos^{2}A+1$

To prove the equality LHS=RHS

$cos4A=8cos^{4}A-8cos^{2}A+1$

Let us take LHS

$cos4A=cos2(2A)$

$=2cos^{2}2A-1$  (since using $cos2A=2cos^{2}A-1$  here A=2A)

$=2[(2cos^{2}2A-1)^2]-1$

$=2[2^2cos^{4}2A-2\times 2cos^{2}2A+1]-1$ (using the formula $(a-b)^2=a^2-2ab+b^2$ here $a=2cos^{2}2A$ and b=1)

$=2[4cos^{4}2A-4cos^{2}2A+1]-1$  

$=8cos^{4}2A-8cos^{2}2A+2-1$

$=8cos^{4}2A-8cos^{2}2A+1$

$=8cos^{4}2A-8cos^{2}2A+1=RHS$

$cos4A=8cos^{4}2A-8cos^{2}2A+1=RHS$

Therefore LHS=RHS.

We proved the equality $cos4A=8cos^{4}A-8cos^{2}A+1$ is true and hence proved.