Question

已知函数f(x)=1-根号2sin(2x-4分之派)除以cosx

有详细的过程~~~~~ 并要求:1.求f(x)的定义域? 2.如果a是第四象限的角,且tan a=(-3分之4),求f(a)的值

Answer 1

∵tana=-4/3 ==> sina/cosa=-4/3
==> sina=-4/3cosa,
∴由sin�0�5a+cos�0�5a=1得
(-4/3cosa)�0�5+cos�0�5a=1
==> cos�0�5a=9/25
∵a为第四象限的角，
∴cosa=3/5。
∴sina=-4/3cosa=-4/5.
故f(a)=（1-√2sin(2a-π/4))/cosa
=(1-√2(sin(2a)cos(π/4)-cos(2a)sin(π/4)))/cosa
=(1-sin(2a)+cos(2a))/cosa
=(1-2sinacosa+2cos�0�5a-1)/cosa
=(-2sinacosa+2cos�0�5a)/cosa
=2(cosa-sina)
=2(3/5+4/5)
=2*7/5
=14/5.

Answer 2

∵tana=-4/3
==>
sina/cosa=-4/3
==>
sina=-4/3cosa,
∴由sin²a+cos²a=1得
(-4/3cosa)²+cos²a=1
==>
cos²a=9/25
∵a为第四象限的角，
∴cosa=3/5。
∴sina=-4/3cosa=-4/5.
故f(a)=（1-√2sin(2a-π/4))/cosa
=(1-√2(sin(2a)cos(π/4)-cos(2a)sin(π/4)))/cosa
=(1-sin(2a)+cos(2a))/cosa
=(1-2sinacosa+2cos²a-1)/cosa
=(-2sinacosa+2cos²a)/cosa
=2(cosa-sina)
=2(3/5+4/5)
=2*7/5
=14/5.