`a) M=sin^2 10^\circ+sin^2 20^\circ+sin^2 45^\circ+sin^2 70^\circ+sin^2 80^\circ`
`M=sin^2 10^\circ+sin^2 20^\circ+sin^2 45^\circ+cos^2 20^\circ+cos^2 10^\circ`
`M=(sin^2 10^\circ+cos^2 10^\circ)+(sin^2 20^\circ+cos^2 20^\circ)+(sin45^\circ)^2`
`M=1+1+(\sqrt{2}/2)^2`
`M=2+1/2`
`M=5/2`
`b) N=tan 35^\circ. tan40^\circ. tan45^\circ. tan50^\circ.tan55^\circ`
`N=tan 35^\circ. tan40^\circ. tan45^\circ. cot 40^\circ.cot35^\circ`
`N=(tan35^\circ.cot35^\circ).(tan40^\circ.cot40^\circ).tan45^\circ`
`N=1.1.1=1`
`c) P=sin^2 42^\circ+sin^2 43^\circ+sin^2 44^\circ+sin^2 45^\circ+sin^2 46^\circ+sin^2 47^\circ+sin^2 48^\circ`
`P=sin^2 42^\circ+sin^2 43^\circ+sin^2 44^\circ+sin^2 45^\circ+cos^2 44^\circ+cos^2 43^\circ+cos^2 42^\circ`
`P=(sin^2 42^\circ+cos^2 42^\circ)+(sin^2 43^\circ+cos^2 43^\circ)+(sin^2 44^\circ+cos^2 44^\circ)+(sin45^\circ)^2`
`P=1+1+1+(\sqrt{2}/2)^2`
`P=3+1/2`
`P=7/2`
`d) Q=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`
`Q=cos^2 15^\circ-cos^2 25^\circ+cos^2 35^\circ-cos^2 45^\circ+sin^2 35^\circ-sin^2 25^\circ+sin^2 15^\circ`
`Q=(cos^2 15^\circ+sin^2 15^\circ)-(cos^2 25^\circ+sin^2 25^\circ)+(cos^2 35^\circ+sin^2 35^\circ)-(cos 45^\circ)^2`
`Q=1-1+1-(\sqrt{2}/2)^2`
`Q=1-1/2`
`Q=1/2`
