Question #d87b9

1 Answer
P dilip_k
Dec 18, 2016

LHS=Cos^2 (pi/8)+cos^2 ((3pi)/8)+cos^2 ((5pi)/8)+ cos^2 ((7pi)/8 )

=Cos^2( pi/8)+cos^2(pi/2-pi/8)+cos^2 ((5pi)/8)+ cos^2 ((3pi)/2-(5pi)/8 )

=Cos^2( pi/8)+(-sin(pi/8))^2+cos^2 ((5pi)/8)+ sin^2 ((5pi)/8 )

=Cos^2( pi/8)+sin^2(pi/8)+cos^2 ((5pi)/8)+ sin^2 ((5pi)/8 )

=1+1=2=RHS

Proved

Related questions
See all questions in Trigonometric Functions of Any Angle
Impact of this question
4986 views around the world
You can reuse this answer
Creative Commons License