Question

to prove that under root 2 + under root 2 + under root 2 + 2 cos 8 theta is equals to 2 cos​

Answer 1

Answer:

Firstly, 2+2cos8θ=2+2(2cos24θ−1)=4cos24θ

∴2+2+2+2cos8θ−−−−−−−−−√−−−−−−−−−−−−−√−−−−−−−−−−−−−−−−−−√=2+2+2cos4θ−−−−−−−−−√−−−−−−−−−−−−−√

Then, 2+2cos4θ=2+2(2cos22θ−1)=4cos22θ

∴2+2+2cos4θ−−−−−−−−−√−−−−−−−−−−−−−√=2+2cos2θ−−−−−−−−−√

Finally, 2+2cos2θ=2+2(2cos2θ−1)=4cos2θ

∴2+2+2cos2θ−−−−−−−−−√−−−−−−−−−−−−−√=4cos2θ−−−−−√=2cosθ