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3 years ago

How would you verify the trigonometric identity 2x = 2sinx cosx

Mathematics

2 answers:

ad-work [718]3 years ago

7 0

Answer:

Step-by-step explanation:

2x = 2sinx cosx is not an identity. An identity is "always true," whereas a conditional equation is true only for specific value(s) of the unknown. Double check to ensure that you have copied down this problem correctly.

dem82 [27]3 years ago

5 0

Step-by-step explanation:

Hi, there!!

I hope you mean sin2x=2sinx . cosx

so, let's begin in a simple way; by adding, alright:

sin2x= sin(x+x) (as 2x=x+x).

now, let's use compound formula for sin,

so, we get:

sin (x+x)= sinx.cosx + cosx. sinx (as sin(A+B)=sin A. cosB + cosA . sinB)

or, sin (x+x)=2sinx.cosx (adding both).

Therefore, sin 2x = 2sinx. cosx.

Hope it helps..

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Jane earns a 5.5% commission on the selling price of each home she sells. She earned $9,020 in commission on the sale of a home.

ratelena [41]

Answer:

"$164000" is the appropriate answer.

Step-by-step explanation:

Let the selling price be "s".

As per the question,

If Jane take 5.5% of selling price i.e.,

= $0.055\times s$

Given commission,

= $9,020

then,

The selling price will be:

⇒ $0.055\times s=9020$

$s=\frac{9020}{0.055}$

$=164000$ ($)

6 0

2 years ago

If < A and < B are vertical angles, and < A = 2x - 11 degrees, and < B = x + 7 degrees, find x.

Tema [17]

Answer:

x=18

Step-by-step explanation:

Vertical angles are congruent. This means that they are equal to each other. So, to solve set them equal to each other and isolate x. First, set up the equation. Then, subtract x from both sides. Finally, add 11 to both sides and simplify.

1) $2x-11=x+7$

2) $x-11=7$

3) $x=18$

7 0

3 years ago

Please help! A-level maths.

astra-53 [7]

$x+y=k\implies y=k-x$

Substitute this into the parabolic equation,

$k-x=6-(x-3)^2\implies x^2-7x+(k+3)=0$

We're told the line $x+y=k$ intersects $C$ twice, which means the quadratic above has two distinct real solutions. Its discriminant must then be positive, so we know

$(-7)^2-4(k+3)=49-4(k+3)>0\implies k$

We can tell from the quadratic equation that $C$ has its vertex at the point (3, 6). Also, note that

$-1\le\sin t\le1\implies3\le3+2\sin t\le5\implies3\le x\le5$

and

$-1\le\cos2t\le1\implies2\le4+2\cos2t\le6\implies2\le y\le6$

so the furthest to the right that $C$ extends is the point (5, 2). The line $x+y=k$ passes through this point for $2+5=k\implies k=7$ . For any value of $k$ , the line $x+y=k$ passes through $C$ either only once, or not at all.