Question

What are the important trigonometric formulas of 1th?

Answer 1

Identity 1:

{\displaystyle \sin ^{2}(x)+\cos ^{2}(x)=1} \sin^2(x) + \cos^2(x) = 1

The following two results follow from this and the ratio identities . To obtain the first
, divide both sides of

{\displaystyle \sin ^{2}(x)+\cos ^{2}(x)=1} \sin^2(x) + \cos^2(x) = 1 by {\displaystyle \cos ^{2}(x)} \cos ^{2}(x); for the second, divide by {\displaystyle \sin ^{2}(x)} \sin^2(x).

{\displaystyle \tan ^{2}(x)+1\ =\sec ^{2}(x)} \tan ^{2}(x)+1\ =\sec ^{2}(x)

{\displaystyle 1\ +\cot ^{2}(x)=\csc ^{2}(x)} 1\ +\cot ^{2}(x)=\csc ^{2}(x)

Similarly

{\displaystyle 1\ +\cot ^{2}(x)=\csc ^{2}(x)} 1\ +\cot ^{2}(x)=\csc ^{2}(x)
{\displaystyle \csc ^{2}(x)-\cot ^{2}(x)=1} {\displaystyle \csc ^{2}(x)-\cot ^{2}(x)=1}