`a) M=cos^2 15^\circ+cos^2 25^\circ+cos^2 35^\circ+cos^2 45^circ+cos^2 55^\circ+cos^2 65^\circ+cos^2 75^\circ`
`M=sin^2 75^\circ+sin^2 65^\circ+sin^2 55^\circ+cos^2 45^\circ+cos^2 55^\circ+cos^2 65^\circ+cos^2 75^\circ`
`M=(sin^2 75^\circ+cos^2 75^\circ)+(sin^2 65^\circ+cos^2 65^\circ)+(sin^2 55^\circ+cos^2 55^\circ)+(sqrt{2}/2)^2`
`M=1+1+1+1/2`
`M=7/2`
`b) N=sin^2 10^\circ-sin^2 20^\circ+sin^2 30^\circ-sin^2 40^\circ-sin^2 50^\circ-sin^2 70^\circ+sin^2 80^\circ`
`N=cos^2 80^\circ-cos^2 70^\circ+sin^2 30^\circ-cos^2 50^\circ-sin^2 50^\circ-sin^2 70^\circ+sin^2 80^\circ`
`N=(cos^2 80^\circ+sin^2 80^\circ)-(cos^2 70^\circ+sin^2 70^\circ)-(cos^2 50^\circ+sin^2 50^\circ)+(1/2)^2`
`N=1-1-1+1/4`
`N=-3/4`
