Question

cho \(sin\alpha=\frac{1}{4}\). tính giá trị biểu thức A=(sin4a+2sin2a).cosa

Answer 1

\(A=\left(2sin2a.cos2a+2sin2a\right)cosa\)

\(=2sin2a.cosa\left(cos2a+1\right)=4sina.cosa.cosa\left(1-2sin^2a+1\right)\)

\(=4sina.cos^2a\left(2-2sin^2a\right)=8sina\left(1-sin^2a\right)\left(1-sin^2a\right)\)

\(=8sina.\left(1-sin^2a\right)^2=8.\frac{1}{4}\left(1-\frac{1}{16}\right)^2=...\)