If 345deg = 300deg + 45deg find tan 345deg

Use the sum formula for tangents:

tan(a+b)=(tan(a)+tan(b))/(1-tan(a)tan(b))

It will be the same as -tan 15.

They probably want you to use the formula

tan(x+y) = [tanx + tany]/[1 - tanx*tany]

tan 300 = -tan 60 = -sqrt3
tan 45 = 1

tan 345 = (1 - sqrt3)/[1 + sqrt3)
= (1 - sqrt3)^2/(1-3)
= (-1/2)(sqrt3 -1)^2 = -0.26795

To find the value of tan 345 degrees, we can use the tangent addition formula:

tan (A + B) = (tan A + tan B) / (1 - tan A * tan B)

In this case, A = 300 degrees and B = 45 degrees.

First, we need to find the values of tan 300 degrees and tan 45 degrees.

To find tan 300 degrees, we can use the fact that the tangent of an angle is equal to the sine of the angle divided by the cosine of the angle:

tan 300 degrees = sin 300 degrees / cos 300 degrees

Next, we use the unit circle to determine the values of sin 300 degrees and cos 300 degrees.

On the unit circle, sin 300 degrees is equal to -0.5 and cos 300 degrees is equal to √3/2.

So, tan 300 degrees = (-0.5) / (√3/2) = -√3 / 3.

Next, we need to find the value of tan 45 degrees.

On the unit circle, sin 45 degrees and cos 45 degrees are equal to 1/√2.

So, tan 45 degrees = (1/√2) / (1/√2) = 1.

Now, we can substitute these values into the tangent addition formula:

tan 345 degrees = (tan 300 degrees + tan 45 degrees) / (1 - tan 300 degrees * tan 45 degrees)

tan 345 degrees = (-√3 / 3 + 1) / (1 - (-√3 / 3 * 1))

Simplifying this expression further will give you the exact numerical value of tan 345 degrees.