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Question

What is hexagon of trigonometric identities?


Solution


Reading across diagonals gives you inverses:
sinx=1cscx
cosx=1secx
tanx=1cotx
Reading from Left to Right gives you these identities:
sin2x+cos2x=1
1+tan2x=sec2x
1+cot2x=csc2x
Reading clockwise or counter-clockwise gives you these ratios:
sinx=cosxcotx
or
sinx=tanxsecx
and so forth...
Reading a function and multiplying the two nearest neighbors gives you these identities:
sin x = cos x . tan x
cos x = sin x . cot x
tan x = sin x . sec x
and so forth
Relations can be dervied too. Ratio of any two left-right neighbours is the same:
sinxcosx=tanx1=1cotx=secxcscx

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