Cos(A-B) = cosAcosB + sinAsinB
<span>
cos(</span>π/2 - θ) = cos(π/2)cosθ + sin(π/2)sinθ
π/2 = 90°
cos(π/2) = cos90° = 0. sin(π/2) = sin90° = 1
cos(π/2 - θ) = cos(π/2)cosθ + sin(π/2)sin<span>θ
</span>
= 0*cosθ + 1*sin<span>θ = </span>sin<span>θ
Therefore </span>cos(π/2 - θ) = sin<span>θ
QED </span>
Answer:
10
Step-by-step explanation:
radius is the middle point of a circle, therefore divide it in half.
Number of proper subsets = 2^number of elements- 1
= 2^n - 1
No of elements = 4
2^4-1 = 16-1 = 15
Answer:
64π m³
Step-by-step explanation:
The general formula for the volume of a cylinder:
V = πr²h, where 'r' is the radius and 'h' is the height
In the given problem, the radius is equal to 4 m and the height is equal to 4 m. Plugging these values into the equation:
V = π4²(4) = π16*4 = 64π m³
Answer:
x = 38, y = 4
Step-by-step explanation:
Since AB = BC then the triangle is isosceles and the base angles are congruent, that is
∠ DAB = ∠ DCB = 52°
Subtract the sum of the base angle from 180° for ∠ ABC
∠ ABC = 180° - (52 + 52)° = 180° - 104° = 76°
Note that ∠ ABD = ∠ CBD, thus
x = 76 ÷ 2 = 38
BD bisects the side AC, thus DC = AD = 4
Thus y = 4
