Trigometric Inverse Functions Formula

 

Sin^-1𝜽  = 1/ Cosec^-1𝜽       OR     Cosec^-1𝜽 = 1/  Sin^-1𝜽 

Sec^-1𝜽  = 1/ Cos^-1𝜽       OR     Cos^-1𝜽 = 1/  Sec^-1𝜽 

Tan^-1𝜽  = 1/ Cot^-1𝜽       OR     Cot^-1𝜽 = 1/  Tan^-1𝜽 

 Sin^-1(-𝜽) = Sin^-1𝜽

Cos^-1(-𝜽) = 𝝅 - Cos^-1𝜽 

Tan^-1(-𝜽) = -Tan^-1𝜽

Sin^-1(Sin𝜽) = 𝜽,   Cos^-1(Cos𝜽) = 𝜽 

Tan^-1(Tan𝜽) = 𝜽,  Cot^-1(Cot𝜽) = 𝜽  

Sec^-1(Sec𝜽) = 𝜽,   Cosec^-1(Cosec𝜽) = 𝜽

  Equations:-

Sin^-1𝜽 + Cos^-1𝜽  = 𝝅/𝟐
Tan^-1𝜽 + Cot^-1𝜽  = 𝝅/𝟐
Sec^-1𝜽 + Cosec^-1𝜽 = 𝝅/𝟐

Sin^-1x = Cos^-1√𝟏-x = Tan^-1(x/√𝟏-x² )

Cos^-1x = Sin^-1√𝟏-x = Tan^-1(√𝟏-x²/x )

Tan^-1x = Sin^-1(x/√𝟏+x²) = Cos^-1(1/√𝟏+x²)

2Sin^-1x = Sin^-1(2x.√𝟏-x²) 

2Cos^-1x = Cos^-1(2x²-1x²) 

2Tan^-1x = Sin^-1(2x/𝟏+x²) = Cos^-1()1/√𝟏+x²