cos^2(pi/8)+cos^2(3pi/8)+cos^2(5pi/8)+cos^2(7pi/8) can you solve it showing me the whole way of how doing it?
cos2(π8)+cos2(3π8)+cos2(5π8)+cos2(7π8) cos2(12⋅π4)+cos2(12⋅3π4)+cos2(12⋅5π4)+cos2(12⋅7π4)
Apply the half-angle formula: cos2(12⋅a)=12(1+cosa)
12(1+cosπ4)+12(1+cos3π4)+12(1+cos5π4)+12(1+cos7π4)
Now we can evaluate the cosines.
12(1+√22)+12(1−√22)+12(1−√22)+12(1+√22)
Simplify.
(1+√22)+(1−√22) 1+√22+1−√22 2
If you want more steps shown please just say so
cos2(π8)+cos2(3π8)+cos2(5π8)+cos2(7π8) cos2(12⋅π4)+cos2(12⋅3π4)+cos2(12⋅5π4)+cos2(12⋅7π4)
Apply the half-angle formula: cos2(12⋅a)=12(1+cosa)
12(1+cosπ4)+12(1+cos3π4)+12(1+cos5π4)+12(1+cos7π4)
Now we can evaluate the cosines.
12(1+√22)+12(1−√22)+12(1−√22)+12(1+√22)
Simplify.
(1+√22)+(1−√22) 1+√22+1−√22 2
If you want more steps shown please just say so
Very ingenious, hectictar.....it would not have occurred to me to apply the half-angle formula!!!!
cos^2(pi/8)+cos^2(3pi/8)+cos^2(5pi/8)+cos^2(7pi/8)
can you solve it showing me the whole way of how doing it?
cos2(18π)+cos2(38π)+cos2(58π)+cos2(78π)= ?
cos(78π)=cos(π−18π)=−cos(18π)cos(58π)=cos(π−38π)=−cos(38π)
cos2(18π)+cos2(38π)+cos2(58π)+cos2(78π)=cos2(18π)+cos2(38π)+[−cos(38π)]2+[−cos(18π)]2=cos2(18π)+cos2(38π)+cos2(38π)+cos2(18π)=2⋅(cos2(18π)+cos2(38π))|cos(38π)=sin(12π−38π)=sin(18π)=2⋅(cos2(18π)+sin2(18π)⏟=1)=2
cos^2(pi/8)+cos^2(3pi/8)+cos^2(5pi/8)+cos^2(7pi/8)
can you solve it showing me the whole way of how doing it?
cos2(18π)+cos2(38π)+cos2(58π)+cos2(78π)=?
cos(38π)=sin(12π−38π)=sin(18π)cos(58π)=sin(12π−58π)=−sin(18π)=−sin(π−18π)=−sin(78π)
cos2(18π)+cos2(38π)+cos2(58π)+cos2(78π)=cos2(18π)+[sin(18π)]2+[−sin(78π)]2+cos2(78π)=cos2(18π)+sin2(18π)⏟=1+sin2(78π)+cos2(78π)⏟=1=1+1=2