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pl show me how to solve with all the steps.
i'll give you brainliest and pts
sin 18° = (√5 - 1)/4

Answer is in the explanation.

Step-by-step explanation:

We are going to find in terms of using Pythagorean Identity: .

Subtract on both sides:

Take square root of both sides:

We are going to use the positive one since 18 is in the first quadrant.  Sine value and cosine value are both positive there:

Now we are going to find a way to use the unit circle.

I know 18 is a factor of 90 because it goes into it 5 times with no remainder.

So let’s use that:

 (sin(90 deg) is 1)

We are going to expand this using and sine addition identity:

Apply double angle identities for both sine and cosine:

Before proceeding I’m going to go ahead and replace with and with :

Apply double angle identities again:

Before proceeding I’m going to go ahead and replace with and with :

This is all in terms of x. Let’s see if this comes out to be a nice polynomial equation:

I’m going to use in the first term on the right hand side that: :

Distribute:

I don’t really see an easy fun math trick here so I’m going to expand everything and put right hand side into standard form:

Gather like terms:

Simplify the gatherings:

Subtract 1 on both sides:

A solution by observation is x=1.

Let’s use synthetic division to see if we can find other factors of the right hand side besides the x-1:

1 |  16   0   -20   0    5    -1

  |        16    16  -4   -4     1

      ---------------------------------

      16   16   -4   -4    1      0

The last column shows the remainder is 0 so we have two factors of the right hand side.

That is the right hand side is equal to:

We already know that so the solution must occur in that second factor.

So we are still looking to solve:

.

Use quadratic formula to solve for 2x+1; yes the answer will be in terms of x.  (At this point I’m just curious what route would work because I was lost where to go.)

Multiply both sides by 2x:

Distribute:

Subtract 1 on both sids:

Use quadratic formula to solve for x.  This time the answer will not be in terms of x. :)

20 has a factor that is a perfect square:

Divide top and bottom by 2 since all three terms have a common factor 2:

So we have that x is either:

.

The last solution is negative and recall 18 degrees in the first quadrant so:

That is:

by commutative property.

the answer is 13

step-by-step explanation:

5*5=25

12*12=144

25+144=169

169^2=13

c.

step-by-step explanation:

substitution for (0,1)

y=x^2+4x+1

1=0^2+4(x)0+1

1=0+4(x)0+1

1=4(x)0+1

1=0+1

1=1

substitution for (-3,-2)

y=x+1

-2=-3+1

-2=-2