sinx－（sin3倍的园周率/2－x）＝根号2,则tanx＋cotx为什么.

Question

sinx－（sin 3倍的园周率/2－x）＝根号2,则tanx＋cotx为什么.

Answer 1

sinx-(sin3π/2-x)=√2.
sinx-(-cosx)=√2.
sinx+cosx=√2.
√2sin(x+π/4)=√2.
sin(x+π/4)=1.
sin(x+π/4)=sin(2kπ+π/2),k∈Z.
x+π/4=2kπ+π/2.
x=2kπ+π/2-π/4.
x=2kπ+π/4.
tanx+cotx= tan(2Kπ+π/4)+cot(2kπ+π/4).
=tanπ/4+cotπ/4.
=1+1.
∴ tanx+cotx=2.