Note that since VX and XZ are both line segments, <VWX and <XYZ both equal 180 (also known as a straight angle). Also, note that the sum of the angles in a triangle are 180 degrees. Now, let’s start.

Finding angles of the triangle:

<WYX = <XYZ - <WYZ = 180 - 4x

<XWY = <XWV - <VWY = 180 - 6x

Using the sum of angles in a triangle and substituting these values in:

180 = <X + <WYX + <XWY = 90 + (180 - 4x) + (180-6x) = 450 - 10x

270 = 10x

We are done! I hope this helps! :)

4 0

2 years ago

Simplify <br> cosx ( tanx+cotx)

Soloha48 [4]

The first step to solving this is to use tan(t) = $\frac{sin(t)}{cos(t)}$ to transform this expression.
cos(x) × $( \frac{sin(x)}{cos(x)} + cot(x) )$
Using cot(t) = $\frac{cos(x)}{sin(x)}$ ,, transform the expression again.
cos(x) × $( \frac{sin(x)}{cos(x)} + \frac{cos(x)}{sin(x)} )$
Next you need to write all numerators above the least common denominator (cos(x)sin(x)).
cos(x) × $\frac{sin(x)^{2} + cos(x)^{2} }{cos(x)sin(x)}$
Using sin(t)² + cos(t)² = 1,, simplify the expression.
cos(x) × $\frac{1}{cos(x)sin(x)}$
Reduce the expression with cos(x).
$\frac{1}{sin(x)}$
Lastly,, use $\frac{1}{sin(t)}$ = csc(t) to transform the expression and find your final answer.
csc(x)
This means that the final answer to this expression is csc(x).
Let me know if you have any further questions.
:)

4 0

2 years ago