For positive acute angles AA and B, B, it is known that \tan A=\frac{28}{45}tanA= 45 28 and \cos B=\frac{3}{5}.CosB= 5 3 . Find the value of \cos(A+B)cos(A+B) in simplest form.

The value of is .

Trigonometrically speaking, the sine, cosine and tangent of an angle are described by the following formulas:

(1)

(2)

(3)

Where:

And we have the following trigonometric identity for the cosine of the sum of angles:

(4)

By (1) and (2), we rewrite (4):

If we know that , , and , then the cosine for the sum of angles is:

The value of is .

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Step-by-step explanation:

Given

Required

In trigonometry:

We need to solve for cosA, sinA and sinB

Given that:

and the tangent of an angle is a ratio of the opposite side (x) to the adjacent side (y),

So, we have:

and

For this angle A, we need t calculate its hypotenuse (z).

Using Pythagoras,

From here, we can calculate sin and cos A

and

To angle B.

Give that

and the cosine of an angle is a ratio of the adjacent side (a) to the hypotenuse side (c),

So, we have:

and

For this angle B, we need to calculate its opposite (b).

Using Pythagoras,

Collect like terms

From here, we can calculate sin B

Recall that:

and