Evaluate the following expression given : sin(theta)= 4/5 | cos x = -5/13 tan(theta + x)

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Step-by-step explanation:

From the trigonometry identity:  we have

Given :    and

In the context of the right angle triangle:

The sine of the angle is defined as the ratio of the length of the side that is opposite to the angle divide by the length of the longest side of the triangle i.e, hypotenuse.

∴

The cosine of an angle is the ratio of the length of the side that is adjacent to the angle divided by the length of the hypotenuse.

where =

Using Pythagoras theorem in triangle :   we can find the value of b, where a=4 and c=5.

; =

therefore, the value of

Similarly, we can find tan x ; as also by using Pythagoras we can find the other side as shown in the attachment:

therefore,

on simplify we get:

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3x + 18 = 147°

step-by-step explanation:

3x + 18 = 147°, because the value of the central angle is equal to the value of the arc formed by it.

i hope i you.

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step-by-step explanation: