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2 years ago

Pls help I’ll give brainliest

Mathematics

2 answers:

aksik [14]2 years ago

8 0

Answer:

Step-by-step explanation:

3/2

Andrej [43]2 years ago

7 0

Answer:

$x = \frac{3}{2}$

Step-by-step explanation:

1) Expand.

$- 6x + 8 = - 2x + 2$

2) Add 6x to both sides.

$8 = - 2x + 2 + 6x$

3) Simplify-2x + 2 + 6x to 4x + 2.

$8 = 4x + 2$

4) Subtract 2 from both sides.

$8 - 2 = 4x$

5) Simplify 8 - 2 to 6.

$6 = 4x$

6) Divide both sides by 4.

$\frac{6}{4} = x$

7) Switch sides.

$x = \frac{3}{2}$

Therefor, the answer is option B. 3/2.

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<img src="https://tex.z-dn.net/?f=%5Cfrac%7B%5Csec%5Cleft%28x%5Cright%29%7D%7B%5Ccos%5Cleft%28x%5Cright%29%7D-%5Cfrac%7B%5Csin%5

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Step-by-step explanation:

First, convert all the secants and cosecants to cosine and sine, respectively. Recall that $csc(x)=1/sin(x)$ and $sec(x)=1/cos(x)$ .

Thus:

$\frac{sec(x)}{cos(x)} -\frac{sin(x)}{csc(x)cos^2(x)}$

$=\frac{\frac{1}{cos(x)} }{cos(x)} -\frac{sin(x)}{\frac{1}{sin(x)}cos^2(x) }$

Let's do the first part first: (Recall how to divide fractions)

$\frac{\frac{1}{cos(x)} }{cos(x)}=\frac{1}{cos(x)} \cdot \frac{1}{cos(x)}=\frac{1}{cos^2(x)}$

For the second term:

$\frac{sin(x)}{\frac{cos^2(x)}{sin(x)} } =\frac{sin(x)}{1} \cdot\frac{sin(x)}{cos^2(x)}=\frac{sin^2(x)}{cos^2(x)}$

So, all together: (same denominator; combine terms)

$\frac{1}{cos^2(x)}-\frac{sin^2(x)}{cos^2(x)}=\frac{1-sin^2(x)}{cos^2(x)}$

Note the numerator; it can be derived from the Pythagorean Identity:

$sin^2(x)+cos^2(x)=1; cos^2(x)=1-sin^2(x)$

Thus, we can substitute the numerator:

$\frac{1-sin^2(x)}{cos^2(x)}=\frac{cos^2(x)}{cos^2(x)}=1$

Everything simplifies to 1.

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