Question

已知函数f（x)=sinx+sin[x+（π/2],x∈R若f(a)=3/4 求sin2a的值?

Answer 1

f（x)=sinx+sin[x+（π/2]=sinx+cosx=√2sin2x，所以f(a)=√2sin2a=3/4，所以sin2a=3√2/8

Answer 2

f（x)=sinx+sin[x+（π/2],化简即为f（x)=sinx+cosx,
则f(a)=sina+cosa=3/4,
两边平方得 1+2sina cosa=9/16
则 2sina cosa=-7/16
即sin2a=2sina cosa=-7/16

Answer 3

f（x)=sinx+sin[x+（π/2]

f（x)=sinx+cosx=√2sin(x+π/4)
即√2sin(a+π/4)=3/4
而-sin2a=cos(2a+π/2)=1-2sin²(a+π/4)=7/16
所以sin2a=-7/16

Answer 4

f(a)=3/4小于1所以sin(x+pai/2)=-cosx所以f(a)=sina-cosa=3/4两边平方得-2sinacosa=-7/16所以sin2a=2sinacosa=7/16

Answer 5

7/16 f(a)^2=(sina-cosa)^2=1-sin2a=9/16sin2a=7/16