Question #da913

2 Answers
Jim H
May 7, 2017

Use #cos(2theta) = cos^2(theta)-sin^2(theta)#

Explanation:

#sin^2(pi/5)-cos^2(pi/5) = -(cos^2(pi/5)-sin^2(pi/5))#

# = -(cos(2(pi/5)))#

# = -cos((2pi)/5)#

Y
May 7, 2017

#-cos((2pi)/5)#

Explanation:

Consider the Pythagorean identity:
#sin^2(theta)+cos^2(theta)=1#
which can lead to:
#sin^2(theta)=1-cos^2(theta)#
Next, consider the power-reducing identity for #cos^2(theta)#:
#cos^2(theta)=(1+cos(2theta))/2#

Using the Pythagorean identity and the power reducing identity, we get:
#sin^2(pi/5)-cos^2(pi/5)=1-cos^2(pi/5)-cos^2(pi/5)#
#=1-2cos^2(pi/5)#
#=1-2((1+cos(2(pi/5)))/2)#
#=1-(1+cos((2pi)/5))#
#=1-1-cos((2pi)/5)#
#=-cos((2pi)/5)#

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