Question

tanα=2tan5/π 求cos(α-3/10π)/sin(α-5/π

Answer 1

tanα=2tanπ/5
cos(α-3π/10)/sin(α-π/5)
=(cosαcos3π/10+sinαsin3π/10) / (sinαcosπ/5-cosαsinπ/5)
=(cos3π/10+tanαsin3π/10) / (tanαcosπ/5-sinπ/5)
=(cos3π/10+2tanπ/5sin3π/10) / (2tanπ/5cosπ/5-sinπ/5)
={sin(π/2-3π/10)+2tanπ/5cos(π/2-3π/10) } / (2tanπ/5cosπ/5-sinπ/5)
={sinπ/5+2tanπ/5cosπ/5) } / (2tanπ/5cosπ/5-sinπ/5)
={sinπ/5+2sinπ/5 } / (2sinπ/5-sinπ/5)
=(3sinπ/5)/(sinπ/5)
=3