Trigonometry - Inverse Functions - 1

Sin(sin‾¹x) = x
sin‾¹(sinθ) = θ

Similar relations hold for cos, tan, cosec, sec and cot.


sin‾¹x = cosec‾¹(1/x)
cos‾¹x = sec‾¹(1/x)
tan‾¹x = cot‾¹(1/x)


Relation between f(-x) and f(x)
sin‾¹(-x) = -sin‾¹x
cosec‾¹(x) = -cosec‾¹x

cos‾¹(x) = π - cos‾¹x
secπ -(-x) = π - sec‾¹x

tan‾¹(x) = -tan‾¹x
cot‾¹(-x) = π-cot‾¹x




sin‾¹x + cos‾¹x = π/2
tan‾¹x + cot‾¹x = π/2
sec‾¹x + cosec‾¹x = π/2

sin‾¹x + sin‾¹y = sin‾¹[x*SQRT(1-y²) + y*SQRT(1-x²)]

sin‾¹x-sin‾¹y = sin‾¹[x*SQRT(1-y²) - y*SQRT(1-x²)]

cons‾¹x +‾cos‾¹y = cos‾¹[xy - SQRT(1-x²) SQRT(1-y²)]

cos‾¹x-cos‾¹y = cos‾¹[xy + SQRT(1-x²) SQRT(1-y²)]

tan‾¹x + tan‾¹y =tan‾¹[(x+y)/(1-xy)] if xy<1

tan‾¹x -tan‾¹y = tan‾¹[(x-y)/(1+xy)] if xy>-1



Multiples of inverse functions

2sin‾¹x

2cos‾¹x

2tan‾¹x



3sin‾¹x

3cos‾¹x

3tan‾¹x



tan‾¹ [(1+x)/(1-x)] = π/4+ tan‾¹x

tan‾¹ [(1-x)/(1+x)] = π/4 - tan‾¹x