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Nikitich [7]
2 years ago
6

Verify the following identity and show steps (Cos2 θ)/(1+sin2 θ)= (cot θ-1)/(cot θ+1)

Mathematics
1 answer:
Paul [167]2 years ago
5 0

Answer:

Verified below

Step-by-step explanation:

We want to show that (Cos2θ)/(1 + sin2θ) = (cot θ - 1)/(cot θ + 1)

In trigonometric identities;

Cot θ = cos θ/sin θ

Thus;

(cot θ - 1)/(cot θ + 1) gives;

((cos θ/sin θ) - 1)/((cos θ/sin θ) + 1)

Simplifying numerator and denominator gives;

((cos θ - sin θ)/sin θ)/((cos θ + sin θ)/sin θ)

This reduces to;

>> (cos θ - sin θ)/(cos θ + sin θ)

Multiply top and bottom by ((cos θ + sin θ) to get;

>> (cos² θ - sin²θ)/(cos²θ + sin²θ + 2sinθcosθ)

In trigonometric identities, we know that;

cos 2θ = (cos² θ - sin²θ)

cos²θ + sin²θ = 1

sin 2θ = 2sinθcosθ

Thus;

(cos² θ - sin²θ)/(cos²θ + sin²θ + 2sinθcosθ) gives us:

>> cos 2θ/(1 + sin 2θ)

This is equal to the left hand side.

Thus, it is verified.

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The half-life of iodine-123 is about 13 hours. You begin with 38 grams of iodine-123.
qaws [65]
Half-life, h = 13 hours
Mass initial, a = 38 g
B=base for half-life = 2
(a)
I(t)=a*B^(-t/h)=a*(B^(1/h)^(-t)=a*(B^(-1/13))^t
Substituting values,
I(t)=38*(2^(-1/13))^t
a=38 g
b=2^(-1/13)=0.9480775 (approximately)
=>
I(t)=38*0.9480775^t

(b) I(t)=7
solve
I(t)=7=38*0.948077^t
Take log on both sides and solve for t
t=log(7/38)/log(0.948077)
=31.727 hours.

Check: I(31.727)=38*9.948077^(31.727)=7.000 g  ok
7 0
3 years ago
Calculate the mean average of these 5 numbers 1,2,3,4,5
Vesna [10]

Answer:

The mean is to add up all the numbers then divide by how many there are.

Step-by-step explanation:

Therefore, 1+2+3+4+5=15

15÷5=3

it's 3

hope it helps :)

6 0
2 years ago
If A = (please see image) find the matrix 7A.
vovangra [49]
The second row in the answer
6 0
3 years ago
How do you know that the product 221×331 is rational?
guapka [62]

221 is rational since 221 = 221/1

So is 331 because 331 = 331/1

The product of any two rational numbers is also rational

--------------------------

Proof:

Let x = p/q and y = r/s be two rational numbers. The q and s values are nonzero.

Their product is

x*y = (p/q)*(r/s)

x*y = (p*q)/(r*s)

which is a ratio of two integers pq and rs, so (p*q)/(r*s) is rational

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Answer:

Step-by-step explanation:

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