Plus Two Maths Notes Chapter 2 Inverse Trigonometric Functions is part of Plus Two Maths Notes. Here we have given Plus Two Maths Notes Chapter 2 Inverse Trigonometric Functions.

Board |
SCERT, Kerala |

Text Book |
NCERT Based |

Class |
Plus Two |

Subject |
Maths Notes |

Chapter |
Chapter 2 |

Chapter Name |
Inverse Trigonometric Functions |

Category |
Kerala Plus Two |

## Kerala Plus Two Maths Notes Chapter 2 Inverse Trigonometric Functions

**Inverse Trigonometric Functions**

For suitable values of domain we have:

- y = sin
^{-1 }x ⇒ x = sin y - x = sin y ⇒ y = sin’x
- sin(sin
^{-1 }x) = x - sin
^{-1 }(sin x) = x - similar results exists for other trigonometric functions.
- (i) sin
^{-1}= cos ec^{-1 }x

(ii) cos^{-1}= sec^{-1}x

(iii) tan^{-1}= cot^{-1}x - (i) sin
^{-1 }(-x) = – sirn^{-1 }x

(ii) cos^{-1 }(-x) = π -cos^{-1 }x

(iii) cosec^{-1 }(-x) = -cosec^{-1 }x

(iv) sec^{-1 }(-x) = π – ec^{-1 }x

(v) tan^{-1 }(-x) = – tan^{-1 }x

(vi) cot^{-1 }(-x) = π – cot^{-1 }x - (i) sin
^{-1}^{ }x + cos^{-1 }x =

(ii) cosec^{-1 }x + sec^{-1 }x =

(iii) tan^{-1 }x + cot^{-1 }x =

- To write inverse trigonometrical functions in simplest form,

(i) for , put x = a sinθ or x = a. cosθ

(ii) for , put x = a tanθ or x = a. cotθ

(iii) for , put x=a secθ or x = a. cosecθ

(iv) for and , put x=a cosθ or x = a cos2θ

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