Prove that cos(π/16)=(1/2)√2+√2+√2

Steps to prove cos(π/16)=(1/2)√2+√2+√2

We know that 

⇒2cos^2(π/16)=1+cos(π/8)

⇒2cos^2(π/16)=1+cos√(2+√2/2)

⇒cos^2(π/16)=(2+√2+√3)/4

⇒cos(π/16)=(√2+√2+√3)/2

⇒cos(π/16)=(1/2)√2+√2+√2

Hence cos(π/16)=(1/2)√2+√2+√2 is proved.

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