How do you use the double angle formula to find the exact value of the given expression?

Question

#2cos^2 7pi/8 -1#

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Answer 1 · 2018-02-19T06:55:00

# sqrt2/2~~0.7071#.

Knowing that, #cos2theta=2cos^2theta-1#, we have,

#2cos^2(7pi/8)-1#,

#=cos(2xx7pi/8)=cos(7pi/4)#,

#=cos(2pi-pi/4)#,

#=cos(pi/4)#,

#=sqrt2/2#.

Taking #sqrt2~~1.4142#,

# 2cos^2(7pi/8)-1~~0.7071#.