Cos^2 π/8 + cos^2 3π/8 + Cos^2 5π/8 + cos^2 7π/8 Solve And Answer The Value ?

2 Answers

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

Explanation:

rarrcos^2(pi/8)+cos^2((3pi)/8)+cos^2((5pi)/8)+cos^2((7pi)/8)

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

=cos^2(pi/8)+cos^2((3pi)/8)+cos^2((3pi)/8)+cos^2(pi/8)

=2*[cos^2(pi/8)+cos^2((3pi)/8)]

=2*[cos^2(pi/8)+sin^2(pi/2-(3pi)/8)]

=2*[cos^2(pi/8)+sin^2(pi/8)]=2*1=2

Apr 28, 2018

2.

Explanation:

Here is another solution, using the Identity :

1+cos2theta=2cos^2theta.............(ast)

We know that, cos(pi-theta)=-costheta.

:. cos(5/8pi)=cos(pi-3/8pi)=-cos(3/8pi),"&, likewise, "

cos(7/8pi)=-cos(1/8pi).

"Hence, the reqd. value"=2cos^2(1/8pi)+2cos^2(3/8pi),

={1+cos(2*1/8pi)}+{1+cos(2*3/8pi)}......[because, (ast)],

=2+cos(1/4pi)+cos(3/4pi),

=2+cos(1/4pi)+cos(pi-1/4pi),

=2+cos(1/4pi)-cos(1/4pi),

=2, as Respected Abhishek K. has already derived!