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slavikrds [6]
2 years ago
8

Simplify the expression using trigonometric identities:

Mathematics
1 answer:
Anastaziya [24]2 years ago
3 0

The simplified expression is the one in option B.

<h3>How to simplify the expression?</h3>

Remember that:

sec(x) = 1/cos(x)\\\\cos(x) = cos(-x)

With these two, we can rewrite the numerator as:

sec(x)*sin(-x) + tan(-x)\\\\\frac{1}{cos(x)}*sin(-x) + tan(x)\\\\\frac{1}{cos(-x)}*sin(-x) + tan(-x)\\\\2*tan(-x)

Replacing that in the given expression, we have:

\frac{2*tan(-x)}{1 + sec(-x)} = \frac{2*tan(-x)}{1 + 1/cos(-x)}

Now, if we multiply and divide by cos(-x), we get:

\frac{2*tan(-x)}{1 + 1/cos(-x)} =  \frac{2*tan(-x)}{1 + 1/cos(-x)}*\frac{cos(-x)}{cos(-x)} \\\\= \frac{2*sin(-x)}{1 + cos(-x)}

Now remember that:

cos(x) = cos(-x)\\sin(-x) = -sin(x)

With these two properties:

\frac{2*sin(-x)}{1 + cos(-x)} = \frac{-2*sin(x)}{1 + cos(x)}

Then the correct option is B.

If you want to learn more about trigonometric identities:

brainly.com/question/7331447

#SPJ1

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Answer:

F = -6 + 2d/5

Step-by-step explanation:

2d-5f=30

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-5f=30-2d

divide both sides by -5

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3 years ago
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suppose someone tells you that she has a triangle with sides having lengths 2.6,8.1 and 8.6. Is this a right triangle? why or wh
sveta [45]
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How do we determine which length is the hypotenuse, though? Knowledge that the hypotenuse is always the longest length of a right triangle helps here, as we can clearly observe that 8.6 is the longest we've been given for this problem. The order we pick the legs in doesn't matter, since addition is commutative, and we'll get the same result regardless of the order we're adding a and b.

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Performing the necessary calculations, we have:

6.76 + 65.61 = 73.96
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Failing this, we know that our triangle cannot be right, but we <em>do </em>know that 72.37 < 73.96, which tells us something about what kind of triangle it is. Imagine taking a regular right triangle and stretching its hypotenuse, keeping the legs a and b the same length. This has the fact of <em>increasing the angle between a and b</em>. Since the angle was already 90°, and it's only increased since then, we know that the triangle has to be <em>obtuse</em>, which is to say: yes, there's an angle in it larger than 90°.
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3 years ago
What percent is equivalent to the fraction and decimal below? Enter your
adoni [48]

Answer:

Percent = 20%

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Therefore, 20% is our answer.

Hoped this helped.

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2 years ago
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lora16 [44]

Answer:

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Step-by-step explanation:

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7 0
2 years ago
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How do you factorise 14x -21xy
alexandr402 [8]
<span>Simplifying 14x + -21xy
 
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Final result:
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