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How to Solve If Tan Inverse X + Tan Inverse Y: How to Have Fun With This Question

How to Solve If Tan Inverse X + Tan Inverse Y: How to Have Fun With This Question

How to solve the if Tan Inverse X + Tan Inverse Y question? You might be asking yourself why do I need to know this equation? 

The answer is that you probably don’t need to know this equation, but it’s fun and can be used in lots of different ways! This article will show you how to use this fun math equation in ways that will benefit your life, even if you never need to write it down again! To start off, 

let’s have some fun with this question!

3 The basic solution

To solve tan ( inverse X + inverse Y), we must first isolate inverse X and inverse Y by multiplying them by themselves. Both of these expressions will result in a product that equals 1/y. We can now add these two products together for our final answer, tan(inverseX+inverseY).


1) Solve each of your tan inverse functions individually. 

2) Solve for (X,Y). 3) Set your solution equal to each other and then solve for Z.


Using basic trigonometry and some algebra, we can solve for tan inverse x. First, add tan inverse x and tan inverse y to both sides of the equation. 

Then use a little algebra trickery (dividing by sin(inverse x) and multiplying by cos(inverse x)) to cancel out all of those sines and cosines. 

You’ll be left with 1 + sin2(inverse x) = 2sin2(inverse y). Solving for cosec2(inverse y), you get that cosec2(inverse y) = (1 + sin2(inverse x))/sin2(inverse y). 

Now you have all three pieces of your answer!

What about angle instead of tangent?

The tan of an angle is easy enough to remember but what about if you’re asked for inverse tangent? 

Also known as arcsine, it gets even more complicated when there are two angles. 

Remember that arctangent (the inverse function) is found using arccos, so substitute 'arccos' in for tan in either angle 

and use a calculator - or don't! Knowing how to solve directly can save you time and often gives you a better answer.

What about inverse tangents?

If you’re reading a question on a test, look for inverse tangents. A question about inverse tangents can be rephrased as a question about tangent inverses. 

To solve a problem with inverse tangents, take Tan inverses of tan (x) and tan (y) and divide them by their common factors, then simplify. Sometimes there are only one or two common factors.

Another fun way to solve it

Let’s say that you had a triangle with sides 3, 4, and 5. The tangent of an angle is one over the opposite side times the sine of that angle.


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