1)
LHS = cot(a/2) - tan(a/2)
= (1 - tan^2(a/2))/tan(a/2)
= (2-sec^2(a/2))/tan(a/2)
= 2cot(a/2) - cosec(a/2)sec(a/2)
= 2(1+cos(a))/sin(a) - 1/(cos(a/2)sin(a/2))
= 2 (1+cos(a))/sin(a) - 2/sin(a)) (product to sums)
= 2[(1+cos(a) -1)/sin(a)]
=2cot a
= RHS
2.
LHS = cot(b/2) + tan(b/2)
= [1 + tan^2(b/2)]/tan(b/2)
= sec^2(b/2)/tan(b/2)
= 1/sin(b/2)cos(b/2)
using product to sums
= 2/sin(b)
= 2cosec(b)
= RHS
Volume of a rectangular prism = l × w × h.
In this case,
V = 270 cubic feet
l = 15 feet
w = 4 ft
h = ?
Plug our values into the volume formula.
270 cubic feet = 15 feet × 4 feet × h.
Simplify the right side
270 = 60 × h.
Divide each side by 60.
4.5 = h
The height is 4.5 feet.
Answer:
The answer is A.
Step-by-step explanation:
Lets call f(x)=y, so y= 4*(3*x-5), we want to find 'x', using 'y' as a the variable.
Now lets change the name of 'y' to 'x', and 'x' to f^-1(x).
f-1(x) = (x+20)/12
Answer:
200 + 50x = 450
Step-by-step explanation:
So, 200 + 50x = 450
50x = 450-200 = 250
X = 250/50
X = 5
Check:
200 + 50(5)
= 200 + 250 = 450.
