Hello,
Here is the demonstration in the book Person Guide to Mathematic by Khattar Dinesh.
Let's assume
P=cos(a)*cos(2a)*cos(3a)*....*cos(998a)*cos(999a)
Q=sin(a)*sin(2a)*sin(3a)*....*sin(998a)*sin(999a)
As sin x *cos x=sin (2x) /2
P*Q=1/2*sin(2a)*1/2sin(4a)*1/2*sin(6a)*....
*1/2* sin(2*998a)*1/2*sin(2*999a) (there are 999 factors)
= 1/(2^999) * sin(2a)*sin(4a)*...
*sin(998a)*sin(1000a)*sin(1002a)*....*sin(1996a)*sin(1998a)
as sin(x)=-sin(2pi-x) and 2pi=1999a
sin(1000a)=-sin(2pi-1000a)=-sin(1999a-1000a)=-sin(999a)
sin(1002a)=-sin(2pi-1002a)=-sin(1999a-1002a)=-sin(997a)
...
sin(1996a)=-sin(2pi-1996a)=-sin(1999a-1996a)=-sin(3a)
sin(1998a)=-sin(2pi-1998a)=-sin(1999a-1998a)=-sin(a)
So sin(2a)*sin(4a)*...
*sin(998a)*sin(1000a)*sin(1002a)*....*sin(1996a)*sin(1998a)
= sin(a)*sin(2a)*sin(3a)*....*sin(998)*sin(999) since there are 500 sign "-".
Thus
P*Q=1/2^999*Q or Q!=0 then
P=1/(2^999)
The justification:
1.4 · ( -2 ) + 2 = 2 · ( -2 ) + 3.2
-2.8 + 2 = - 4 + 3.2
- 0.8 = - 0.8
Answer: B)
Answer:
33.32 / 9.8 = 3.4;
Step-by-step explanation:
Answer:
Cost price of each cup = 1500/6 = 250
Selling price of each cup = 1650/5 = 330
Step-by-step explanation:
Cost price of cups = 1500
Profit = 10%
Selling price of cups = ?
Profit and loss percentage are calculated based on cost price and the formula to calculate profit is mentioned as under:
Profit percentage (%) = Profit x 100/Cost price
10 = Profit x 100/1500
⇒ Profit = 10 x 1500/100
⇒ Profit = 150
The formula for finding selling price is mentioned as under:
Selling Price = Profit + Cost Price.
Selling Price = 150 + 1500
⇒ Selling Price = 1650.
Since one of the six cups was broken that means the seller earned profit based on only 5 cups, it implies that selling price of each cup will be 1650/5 = 330.
Answer is below :-).......
