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Lyrx [107]
3 years ago
14

Verify the pythagorean identity 1 + c o t ^2 θ = c s c ^2 θ

Mathematics
1 answer:
Grace [21]3 years ago
6 0

Answer: The identity is verified. See the explanation.

Step-by-step explanation:

You must keep on mind the following identities:

csc\theta=\frac{cos\theta}{sin\theta}\\\\csc\theta=\frac{1}{sin\theta}\\\\sin^2\theta+cos^2\theta=1

Therefore, by substitution, you can rewrite the identity as shown below:

1+cot^2\theta=csc^2\theta\\\\1+\frac{cos^2\theta}{sin^2\theta}=csc^2\theta

Simpliying, you obtain:

\frac{sin^2\theta+cos^2\theta}{sin^2\theta}=csc^2\theta\\\\\frac{1}{sin^2\theta}=csc^2\theta\\\\csc^2\theta=csc^2\theta

The identity is verified.

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7 0
2 years ago
(x+16)²=12 plz help me and show work
Readme [11.4K]

Answer:

The answer is x=-16 ±2\sqrt{3} in exact form or x=-12.535898, x=-19.464102 in decimal form.

Step-by-step explanation:

To solve this problem, start by moving all terms to the left side of the equation and simplify. Simplify the equation by subtracting 12 from both sides of the equation and squaring x+16, which will look like x^{2} +32x+256-12=0. Next, simplify the equation again, which will look like x^{2} +32x+244=0.

Then, use the quadratic formula to find the solutions. The quadratic formula looks like\frac{-b(+-)\sqrt{b^{2}-4ac } }{2a}.

For this problem, the quadratic variables are as follows:

a=1

b=32

c=244

The next step is to substitute the values a=1, b=32, and c=244 into the quadratic formula and solve. The quadratic formula will look like \frac{-32(+-)\sqrt{32^2-4(1*244)} }{2*1}. To simplify the equation, start by simplifying the numerator, which will look like x=\frac{-32(+-)4\sqrt{3} }{2*1}. Then, multiply 2 by 1 and simplify the equation, which will look like x=-16(+-)2\sqrt{3}. The final answer is x=-16 ±2\sqrt{3} in exact form. In decimal form, the final answer is x=-12.535898, x=-19.464102.  

6 0
2 years ago
7+ X -9= -15 solve the equation
Aleksandr-060686 [28]
I believe the answer is x=24
6 0
3 years ago
Read 2 more answers
Write 5,256 divided into 52 and show your work
Angelina_Jolie [31]
Set up you question 5256 divided by 56 then write the answer. Finally if you get a remainder put the answer then the remainder
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3 years ago
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