Answer:
D. Pythagorean
Step-by-step explanation:
Given the identity
cos²x - sin²x = 2 cos²x - 1.
To show that the identity is true, we need to show that the left hand side is equal to right hand side or vice versa.
Starting from the left hand side
cos²x - sin²x ... 1
According to Pythagoras theorem, we know that x²+y² = r² in a right angled triangle. Coverting this to polar form, we have:
x = rcostheta
y = rsintheta
Substituting into the Pythagoras firnuka we have
(rcostheta)²+(rsintheta)² = r²
r²cos²theta+r²sin²theta = r²
r²(cos²theta+sin²theta) = r²
(cos²theta+sin²theta) = 1
sin²theta = 1 - cos²theta
sin²x = 1-cos²x ... 2
Substituting equation 2 into 1 we have;
= cos²x-(1-cos²x)
= cos²x-1+cos²x
= 2cos²x-1 (RHS)
This shows that cos²x -sin²x = 2cos²x-1 with the aid of PYTHAGORAS THEOREM
Answer:
23
Step-by-step explanation:
Because 23•23=529 so the square root of 529 is 23.
Answer:
x ∈ [-2, 7]
Step-by-step explanation:
The given equation ...
x^2 -5x -4 ≤ 10
can be rewritten as ...
x^2 -5x -14 ≤ 0
and factored as ...
(x +2)(x -7) ≤ 0
Clearly, the "or equal to" condition will be met when x=-2 and x=7. For values of x between these numbers, one factor is negative and the other is positive. Hence the product will be negative. So, numbers in that interval are the solution set.
x ∈ [-2, 7]
A fraction x/y is a ratio between two numbers x and y.
The ratio is preserved if both x and y are scaled up or down by the same number n.
This means you can obtain any fraction equivalent to x/y by multiplying both x and y by n, i.e. (n*x)/(n*y).
Then we have 1/4 = (2*1)/(2*4) = 2/8, for example.
The answer is 615.4
Hope this helps :)
