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3 years ago

Rewrite sin(x)cos2(x) − sin(x) as an expression containing a single term

Mathematics

1 answer:

Veronika [31]3 years ago

8 0

Answer: -2sin³x

Step-by-step explanation:

cos ( x + y ) = cosx*cosy - sin y*sinx (1)

if x = y (1) could be express as: cos (2x) = cosx*cosx -sinx*sinx

cos 2x = cos²x -sin²x

Then sin(x)*cos2(x) − sin(x) ⇒ sinx * ( cos²x - sin²x ) - sinx

multiplying sinx*cos²x -sin³x -sinx

sinx (commom factor sinx (cos²x -sin²x -1) but 1-cos²x = sin²x

or -1 +cos²x = -sin²x ⇒sinx( -sin²x -sin²x) ⇒sinx (-2sin²x)

-2sin³x

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3 years ago

Consider the following equation: f(x)=x^2+4\4x^2-4x-8 name the vertical asymptote(s)

zhenek [66]

ANSWER

The vertical asymptotes are

$\Rightarrow x=2\:or\:x=-1$

<u>EXPLANATION</u>

We have

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For vertical asymptotes we set the denominator to zero and solve the quadratic equation;

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We split the middle term to obtain,

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3 years ago

Read 2 more answers

A package of 5 crackers contains 205 Calories. How many Calories are in one cracker using a double number line

natulia [17]

Answer:

Step-by-step explanation:

since there are 205 calories in 5 crackers we can represent this as

205/5

we need to find how many calories are in one cracker, so lets take "x" as the # of calories in 1 cracker

$\frac{x}{1} =\frac{205}{5}$

cross multiply

5x=205

divide by 5 on both sides

x=41

41 calories in 1 cracker

Number line:

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2 years ago