Question

[Nguyễn Trịnh Duy Khiêm]

$A=si{n}^2{12}^o+si{n}^2{70}^o-si{n}^2{35}^o+si{n}^2{30}^o+si{n}^2{78}^o-si{n}^2{55}^o+si{n}^2{20}^o$

Answer 1

[Nguyễn Lê Phước Thịnh]

\(A=\left(sin^212^0+sin^278^0\right)+\left(sin^270^0+sin^230^0\right)-\left(sin^235^0+sin^255^0\right)\)

\(=\left(sin^212^0+cos^212^0\right)-\left(sin^235^0+cos^235^0\right)+\left(sin^270^0+sin^230^0\right)\)

\(=1-1+sin^270^0+\dfrac{1}{4}\)

\(=sin^270^0+\dfrac{1}{4}\)