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Trig Identities : Reciprocal and Pythagorean
1 ) sin x + cos x cot x (given) sin x + 1/ tan x + cos x/sin x = 1/ sin x = csc (reciprical identities and simplify) 2 ) tan x + cot x ( given) sin x/ cos x + cos x/ sin x (recripical) sin x/ cos x + sin x cos x = 1/sin x * 1/ cos x (simplify)
Reciprocal Identities csc x = 1 / sin x sec x = 1 / cos x cot x = 1 / tan x tan x = sin x/ cos x cot x = cos x / sin x Pthygorean Identities sin^2 x + cos ^2 x = 1 tan^2 x + 1 = sec ^2 x 1 + cot^2 x = csc x
What I found most interesting because most of these problems are very simple its only the fact that you had to memorize the identities both reciprocal and pthygorean, then after that it was only a matter of plugging in and solving or proving the actual problem. Of coarse there were a few times where it got confusing but you just have to use math manners. :)
Usually in order to solve these equations, you first have to prove what is given (the equations) then you use either the reciprical or pthygorean identitiy (when using pthygorean identity you also use distributing property and combing like terms) then all thats left is to simplify the problem.
