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
x = 100°
In a parallelogram all the interior angles must add up to 360°
Opposite angles of a parallelogram are equal
360° = x + x + 80° + 80°
360° = 2x + 160°
2x = 200°
x = 100°
Alternatively:
x and 80° are corresponding angles because they are on the same line that crosses two parallel lines. Corresponding angles are complementary and add up to 180°.
180° = x + 80°
x = 100°
Answer:
To find the perimeter of a quadralateral on a coordinate plane, use the distance formula to find the length of each side, and then add the lengths. By using this method, you can find the perimeter accurately.
1. perimeter = 4 and area = 1
2. permeter = 8 and area = 4
3. perimeter = 12 and area = 9
4. perimeter = 16 and area = 16
5. perimeter = 20 and area = 25
