How do you simplify #sec35csc55-tan35cot55#?
Apply a bunch of complementary angle identities to get a result of
First, as in just about any trig problem, convert everything to sines and cosines:
We can ignore the first part of this expression and focus on
We can now make some substitutions for
Now we have
Making yet another substitution, we have:
It's looking like a Pythagorean identity might help us here...
I've underlined that last one because it applies to our problem. To see how, simply subtract
And if this equation is supposed to hold for all values of