tanα=3,则cos(π/4-α)=tanα=3,则cos（π/4-α）=

Question

tanα=3,则cos(π/4-α)=
tanα=3,则cos（π/4-α）=

Answer 1

∵tanα=3
∴sinα/cosα=3
sinα=3cosα
又sin²α+cos²α=1
∴9cos²α+cos²α=1
∴cos²α=1/10
∴cosα=√10/10,sinα=3√10/10
或cosα=-√10/10,sinα=-3√10/10
当cosα=√10/10,sinα=3√10/10时
cos(π/4-α)
=cosπ/4cosα+sinπ/4sinα
=√2/2(cosα+sinα)
=√2/2*4√10/10
=2√5/5
当cosα=-√10/10,sinα=-3√10/10时
cos(π/4-α)
=cosπ/4cosα+sinπ/4sinα
=√2/2(cosα+sinα)
=√2/2*(-4√10/10)
=-2√5/5