Question

16. Prove that (1 + cos (1+cos 13) (1+cos ? (1 + cos9π/10)=1/16​

Answer 1

Answer :1/16

1) sin ( pi/10) =(root5 -1)/4

2) sin (3pi/10)=(root5 -1)/4

3) (1-cos2 (Q)) = sin2(Q)

4) cos ( pi-Q) =-cos(Q)

NoW, Moving Swiftly to the given equation.

(1+cos(pi+10) (1+cos (3pi/10) (1+cos (7pi/10) (1+cos (9pi/10)

=(1+ cos (pi/10) (1+cos(7pi/10) (1+cos (7pi/10) (1+cos (pi/10)

=(1-cos2 (pi/10) (1-cos2 (7pi/10)

=sin2 (pi/10) sin2 (7pi/10)

=[(root5-1/4) (root5-1/4)]^2

={5-1/4×4}^2

=1/16.

Thus, required to answer 1/16.

hence proved.

it's your answer my friend