BodhiAI

Nov. 12, 2019
Inverse Trignometric Identities &Principle value of Inverse Trignometric function

**Principle Value of an Inverse Circular Function**

**The value of an inverse circular function which is numerically least and the set of values for which, the domain is uniquely defined is called the principle value of the function.**

** **

**Problem Solving Trick **

**If two equal numerical values with opposite signs are obtained, then the one with positive sign is taken as the principal value of the Inverse circular function. **

**Properties of Inverse Circular Functions**

**P-1 Principle of Reciprocality **

** For x > 0 and provided that the value of x in each case is such that both sides of the equality are meaningful **

** a) **

** b) **

** c) and further similar cases**

**P-2 Self adjusting Property**

** Since, sin ^{-1}x means the principle value of the angle whose sine is x, the formula is valid only when and the formula sin is meaningful only when **

** a) provided **

** sin if **

** b) provided **

** cos if **

** c) provided **

** if **

**P-3 Express one Inverse Circular Function in terms of other **

** a) **

** b) **

** c) **

**P-4 a) where, **

** b) where, **

** c) where, **

** d) where, **

**P-5 a) where, **

** b) where, **

** c) where, **

**P-6 a) **

** b) **

** c) (where, )**

** Reasoning: If xy > 1, then and hence, lies in -π/2 and 0**

** But since, x=>0 an y>=0 therefore, tan- ^{1}x and tan^{-1}y both lie in π/2 and 0**

** **

**P-7 a) **

** b) **

** c) **

**P-8 a) **

** b) **

** c) **