Evaluate using exact values 1-cos45/1+cos45

1 answer:

3 0

Knowing that cos(45°) = 1/√2 is the way forward.

$\frac{1-\frac{1}{\sqrt{2}} }{1+\frac{1}{\sqrt{2}}} = \frac{\sqrt{2}-1}{\sqrt{2}+1} = 3 - 2\sqrt{2}$

The last step in the equation may not be obious, but the trick here is to multiple numerator and denominator with (1-√2), then the denominator has the special product (a+b)(a-b) = a²-b².

You might be interested in

WILL MARK YOU BRAINLIEST !!!!

liq [111]

Answer:

$\overline {PM} \cong \overline {ON}$ because they are opposite sides of a parallelogram.

Step-by-step explanation:

First of all, let us have a look at the definition of a parallelogram.

A parallelogram is a closed 4 sided figure (i.e. a quadrilateral) made up with two pairs of straight lines such that the two pairs are parallel and equal to each other.

For example, let us consider a quadrilateral ABCD as attached in the diagram in answer area.

The two pair of lines are:

AB, DC and BC, AD

For ABCD to be a parallelogram, the lines

AB and DC must be parallel to each other and AB = DC

AND

BC and AD must be parallel to each other and BC = DA

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

In the given question, we are given that the quadrilateral MNOP is a parallelogram.

The two pairs opposite lines are OP, NM and PM, ON.

As per the definition of a parallelogram,

OP and NM must be parallel and equal to each other.