Question

满足sinπ∕5sinⅩ﹢cos4／5πcosⅩ=1∕2的锐角Ⅹ为多少？ A. π∕6 B.7π∕15 C，π∕3 D.2π∕15

Answer 1

B
因为sinπ∕5sinⅩ﹢cos4／5πcosⅩ=1∕2，sinπ∕5sinⅩ-cosπ／5cosⅩ=1∕2
cos（x+π/5）=-1/2
x+π/5=2π/3
x=7π∕15
所以选择B

Answer 2

sinπ∕5sinⅩ﹢cos4／5πcosⅩ=sinπ∕5sinⅩ-cos1／5πcosⅩ=-cos（x+1／5π）=1/2
cos（x+1／5π）=-1/2=cos2/3π
x+1／5π=2/3π
x=7/15π