solve, tan 10 degrees + tan 70 degrees - tan 50 degrees = ....

To solve this equation, we need to use trigonometric properties and identities.

Step 1: Convert degrees to radians
The trigonometric functions in most calculators work in radians, so we need to convert the given degrees into radians. To convert degrees to radians, we use the formula:
radians = (π/180) * degrees

Converting the given degrees into radians:
10 degrees = (π/180) * 10 = π/18 radians
70 degrees = (π/180) * 70 = 7π/18 radians
50 degrees = (π/180) * 50 = 5π/18 radians

Now we can substitute these values back into the equation:
tan(π/18) + tan(7π/18) - tan(5π/18) = ....

Step 2: Use trigonometric identities
We know that tan(x) = sin(x) / cos(x). So let's express each term in the equation using sine and cosine.

tan(π/18) = sin(π/18) / cos(π/18)
tan(7π/18) = sin(7π/18) / cos(7π/18)
tan(5π/18) = sin(5π/18) / cos(5π/18)

Now let's substitute these expressions back into the equation:
sin(π/18) / cos(π/18) + sin(7π/18) / cos(7π/18) - sin(5π/18) / cos(5π/18) = ....

Step 3: Combine the terms
To combine the terms, we need to find a common denominator for the fractions.

The common denominator for cos(π/18), cos(7π/18), cos(5π/18) is cos(π/18) * cos(7π/18) * cos(5π/18).

Now we can rewrite the equation using the common denominator:
(sin(π/18) * cos(7π/18) * cos(5π/18) / cos(π/18) * cos(7π/18) * cos(5π/18)) +
(sin(7π/18) * cos(π/18) * cos(5π/18) / cos(π/18) * cos(7π/18) * cos(5π/18)) -
(sin(5π/18) * cos(π/18) * cos(7π/18) / cos(π/18) * cos(7π/18) * cos(5π/18)) = ....

Step 4: Simplify the equation
With the common denominator, the fractions can be added/subtracted:
(sin(π/18) * cos(7π/18) * cos(5π/18) + sin(7π/18) * cos(π/18) * cos(5π/18) - sin(5π/18) * cos(π/18) * cos(7π/18)) / (cos(π/18) * cos(7π/18) * cos(5π/18)) = ....

Step 5: Use trigonometric angle sum and difference identities
We can simplify the numerator using trigonometric identities like sin(A + B) = sin(A)cos(B) + cos(A)sin(B) and sin(A - B) = sin(A)cos(B) - cos(A)sin(B).

Let's use these identities to simplify the numerator:
= [sin(π/18)cos(7π/18)cos(5π/18) + sin(7π/18)cos(π/18)cos(5π/18)] - sin(5π/18)cos(π/18)cos(7π/18)
= [(sin(π/18)cos(7π/18)cos(5π/18) - sin(7π/18)cos(π/18)cos(5π/18))] - sin(5π/18)cos(π/18)cos(7π/18)
= sin(π/18 - 7π/18)cos(5π/18) - sin(5π/18)cos(π/18)cos(7π/18)

Using the identity sin(A - B) = sin(A)cos(B) - cos(A)sin(B), we can rewrite the numerator:
= - sin(6π/18)cos(5π/18) - sin(5π/18)cos(π/18)cos(7π/18)

Step 6: Simplify further
We can simplify sin(6π/18) and cos(6π/18) using the trigonometric identity sin(2θ) = 2sin(θ)cos(θ).

Let's simplify the numerator:
= - 2sin(3π/18)cos(5π/18) - sin(5π/18)cos(π/18)cos(7π/18)
= - 2sin(π/6)cos(5π/18) - sin(5π/18)cos(π/18)cos(7π/18)

Step 7: Calculate the simplified expression
Now, you can evaluate this expression using the values of sin(π/6) and cos(π/6) which are known.

Plug in the values:
= - 2 * (1/2) * cos(5π/18) - sin(5π/18) * cos(π/18) * cos(7π/18)

Finally, calculate the result to get your answer.