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dangina [55]
4 years ago
11

Simplify: (1− cos^2 x)·(1+ tan^2 x)

Mathematics
1 answer:
fgiga [73]4 years ago
3 0

Answer:(-cos²x+1)x(tan²x+1)

Step-by-step explanation:

(1-cos²x)x(1+tan²x)

(-cos²x+1)x(tan²x+1)

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3 years ago
What is the exact solution for the equation
Nostrana [21]

Answer:

Option C is correct.

Exact solution of  2^{x+2} = 5^{2x} is, \frac{2\ln 2}{2\ln 5 - \ln 2}

Step-by-step explanation:

Given the equation: 2^{x+2} = 5^{2x}

Using logarithmic rules:

  • a^x=b^y ⇒ x \ln a =y \ln b
  • \ln x^a = a\ln x

Given: 2^{x+2} = 5^{2x}

Taking logarithmic both sides:

\ln 2^{x+2} = \ln 5^{2x}

By logarithmic rules;

(x+2) \ln 2 = (2x) \ln 5

Using distributive property i.e a\cdot (b+c) = a\cdot b + a\cdot c

x \ln 2 +2 \ln 2 = 2x \ln 5

Subtract x \ln 2 from both sides we get;

x \ln 2 +2 \ln 2 - x \ln 2= 2x \ln 5 - x \ln 2

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2 \ln 2= 2x \ln 5 - x \ln 2

or

2 \ln 2= x (2\ln 5 - \ln 2)

Divide both sides by (2\ln 5 - \ln 2) we get;

\frac{2\ln 2}{2\ln 5 - \ln 2} = x

Therefore, the exact solution of the given equation is \frac{2\ln 2}{2\ln 5 - \ln 2}


7 0
3 years ago
If 1 liter = 1.057 quarts, how many quarts are in 1 kiloliter
andrezito [222]
<span>If 1 liter = 1.057 quarts, how many quarts are in 1 kiloliter?
1KL X (1L/1000KL) X (1.057quarts/1L) <<< use a calculator
I hope I helped! :)</span>
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4 years ago
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