For the angles α and β in the figures, find cos(α + β)?

Step-by-step explanation:

Let the hypotenuse of the smaller triangle be h units.

Then; from the Pythagoras Theorem.

From the smaller triangle;

and

From the second triangle, let the other other shorter leg of the second triangle be s units.

Then;

and

We now use the double angle property;

we plug in the values to obtain;

Step-by-step explanation:

We know both legs, we can use the tangent trigonometric reason to find the angle.

We know the hypothenuse and the opposite leg. We can use the sin trigonometric reason to find the angle

So, the sum of them is

Then,

Therefore,

step-by-step explanation: