Answer:
We have to prove
sin(α+β)-sin(α-β)=2 cos α sin β
We will take the left hand side to prove it equal to right hand side
So,
=sin(α+β)-sin(α-β) Eqn 1
We will use the following identities:
sin(α+β)=sin α cos β+cos α sin β
and
sin(α-β)=sin α cos β-cos α sin β
Putting the identities in eqn 1
=sin(α+β)-sin(α-β)
=[ sin α cos β+cos α sin β ]-[sin α cos β-cos α sin β ]
=sin α cos β+cos α sin β- sinα cos β+cos α sin β
sinα cosβ will be cancelled.
=cos α sin β+ cos α sin β
=2 cos α sin β
Hence,
sin(α+β)-sin(α-β)=2 cos α sin β
Let m = slope
Use the point-slope formula.
y - y1 = m(x - x1)
Let y1 = 3
Let x1 = 2
y - 3 = 1(x - 2)
Solve for y.
y - 3 = x - 2
y = x - 2 + 3
y = x + 1
Done!
Answer:
96 ft^2.
Step-by-step explanation:
Area of shaded region = area of the original rectangle - area of the one removed
= 8 * 16 - 8*4
= 128 - 32
= 96
