Question

\(\sin^251+\sin^235+\sin^245+\sin^255+\sin^239\)

Answer 1

Sử dụng đẳng thức: \(sinx=cos\left(90^0-x\right)\)

\(sin^251+sin^235+sin^245+sin^255+sin^239\)

\(=sin^251+sin^235+sin^245+cos^2\left(90-55\right)+cos^2\left(90-39\right)\)

\(=sin^251+cos^251+sin^235+cos^235+sin^245\)

\(=1+1+\left(\dfrac{\sqrt{2}}{2}\right)^2=\dfrac{5}{2}\)

Answer 2

\(\sin^251^0+\sin^235^0+\sin45^0+\sin^255^0+\sin^239^0\)

\(=\left(\sin^251^0+\cos^251^0\right)+\left(\sin^235^0+\cos^255^0\right)+\dfrac{\sqrt{2}}{2}\)

\(=\dfrac{4+\sqrt{2}}{2}\)