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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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This involves basic arithmetic calculations and simultaneous equations.

Adamu has 25 Cards

Let the following letters represent the number of cards each has;

A: ADAMU

F: FUNKE

S: SHEHU

K: KWAME

T: TANKO

  • If adamu gives funke 5 cards, he will have as many as tanko. Thus;

A - 5 = T  --- eq 1

  • If funke gives adamu 4 cards, he will have as many as kwame. Thus;

A + 4 = K  --- eq 2

  • Funke and adamu have a total of 13 more cards than the total that kwame and tanko have. Thus;

A + F = K + T + 13   --- eq 3

  • Adamu has 2 cards more than what Shehu has. Thus;

A - 2 = S  --- eq 4

From online research, the Total Number of cards is 134 and not 133. Thus;

A + F + K + S + T = 134  --- eq 5

Let's put A - 5 = T and A + 4 = K in eq 3 to get;

A + F = (A + 4) + (A - 5) + 13

A + F = 2A + 12

F = 2A - A + 12

F = A + 12

Let's put A - 2 = S ; F = A + 12 ; A - 5 = T and A + 4 = K into eq 5 to get;

A + A + 12  + A + 4 + A - 2 + A - 5 = 134

Simplifying gives;

5A + 9 = 134

5A = 134 - 9

5A = 125

A = 125/5

A = 25

Adamu has 25 Cards

5 0
3 years ago
———-<br><br><br> pls help!!<br><br><br><br><br><br> ——-
nalin [4]

According to above graph :

  • g(-4) = 6

so, correct option is C. 6

6 0
2 years ago
Read 2 more answers
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