Adding Frac Trig Fcns: Going from X2/Tan(55) + X2/Tan(75)=87120 to 5.16X2/5.329=87120

[TMcKinney]

I am reviewing for a certification for work and I am unsure about one of the steps in the provided solution. The following are steps in the solution:

1) X²/Tan(55) + X²/Tan(75)=87120
2) 5.16X²/5.329=87120

Can someone help me see how they are getting from step 1 to step 2? Is there a trig identity at work?

 

[tkhunny]

If I had to guess, I'd guess that \(\displaystyle \tan(55º)\cdot\tan(75º) = 5.329\)

What do you suppose happens if we add the two tangents?

We are finding a Common Denominator so the two fractions can be added.

 

[TMcKinney]

I figured it out, thanks tkhunny!

First thing I checked was tan55 x tan75 and somehow got 25... switching over from a TI-89 to an HP35s using RPN has me miscalculating all sorts of stuff.