1.

Find the value of `cos^2. pi/16+cos^2. (3pi)/16+cos^2. (7pi)/16`.

Answer» `L.H.S.=cos^2. pi/16+cos^2.(3pi)/16+cos^2(pi/2-(3pi)/16)`
`+cos^2(pi/2-pi/16)`
`=cos^2.pi/16+cos^2.(3pi)/16+sin^2.(3pi)/16+sin^2.pi/16`
`=(cos^2. pi/16+sin^2. pi/16)+(cos^2(3pi)/16+sin^2(3pi)/16)`
`=1+1=2`


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