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3 years ago

(1 - cosx) (1 + 1/cosx) = sinxtanx

Mathematics

1 answer:

Nataly [62]3 years ago

5 0

Answer:

cos x ≠ 0 ⇔ x ≠ $\frac{pi}{2}+k.pi$ ; k ∈ N

$(1-cosx)(1+\frac{1}{cosx})=sinx.tanx\\\\(1-cosx)(\frac{cosx+1}{cosx})=sinx.\frac{sinx}{cosx}\\\\ \frac{1-cos^{2} x}{cosx} =\frac{sin^{2}x }{cosx}\\\\=>1-cos^{2}x=sin^{2}x$

<=> cos²x + sin²x = 1

⇔ 1 = 1

=> x = { R \ (pi/2 + k.pi); k ∈ N}

Step-by-step explanation:

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Is it true that the integral LaTeX: \int x^2e^{2x}dx ∫ x 2 e 2 x d x can be evaluated using integration by parts? If so, state t

Marysya12 [62]

Answer:

Yes the integral can be evaluated by integration by parts as solved below.

Step-by-step explanation:

$\int x^{2}e^{2x}dx$

Taking algebraic function as first function and exponential function as second function we have

$\int x^{2}e^{2x}dx=x^{2}\int e^{2x}dx-\int (x^{2})'\int e^{2x}dx\\\\=x^{2}\frac{e^{2x}}{2}-\int 2x\times \frac{e^{2x}}{2}dx\\\\\frac{x^{2}e^{2x}}{2}-\int xe^{2x}dx\\\\Now\\\\\int xe^{2x}dx=x\int e^{2x}dx-\int 1\cdot \int e^{2x}dx\\\\=\frac{xe^{2x}}{2}-\int \frac{e^{2x}}{2}dx\\\\\frac{xe^{2x}}{2}-\frac{e^{2x}}{4}\\\\\therefore \int x^{2}e^{2x}dx=\frac{x^{2}e^{2x}}{2}-\frac{xe^{2x}}{2}+\frac{e^{2x}}{4}$

5 0

3 years ago

Help pls i dont have a lot of time

hram777 [196]

Answer:

1. 8 meters

2.1dk

Step-by-step explanation:

6 0

3 years ago

Solve the equation. -10=2y

I am Lyosha [343]

Answer:

y=-5

Step-by-step explanation:

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7 0

3 years ago

Read 2 more answers

I need 5 lines with a undefined slope

algol13

Answer:

x=1

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??I'm pretty sure thats what u wanted

4 0

3 years ago

Mr. Shamir employs two part-time typists, Inna and Jim, for his typing needs. Inna charges $15 an hour and can type 6 pages an h

coldgirl [10]

Answer:

The minimum cost would be 480$ when Inna works for 8 hours and Jim works for 20 hours.

Step-by-step explanation:

We are given the following information in the question:

Charges for 1 hour for Inna = $15

Number of pages typed by Inna in 1 hour = 6

Charges for 1 hour for Jim = $18

Number of pages typed by Jim in 1 hour = 8

Let x be the number of hours Inna work and let y be the number of hours Jim work.

Total cost = $15x + 18y$

We have to minimize this cost.

Then, we can write the following inequalities:

$6x + 8y \geq 208\\x \geq 8\\y \geq 8\\$

The corner points as evaluated from graph are: (8,20) and (24,8)

C(8,20) = 480$

C(24,8) = 504$

Hence, the minimum cost would be 480$ when Inna works for 8 hours and Jim works for 20 hours.

The attached image shows the graph.

3 0

3 years ago