Class 12th

students can check the table for the principal values for all ITFs below;

To understand this, Assume you have a bucket that has infinite number of apples and if your mother asks "give me the apple". How will you figure out which one is "The Apple", she is asking for.

Similarly any inversre trigonometric functions behaves like a Many-one Function; which means,

For Example $\sin^ {-1}\left (\frac {2} {3}\right)$ can have many solutions, we need to fix one solutions which can be used as standerd value for the function.

• A standerd value (Angles) of any inverse trigonometric value lies between a fiexed range is known as principal value. 

For Ex; The value of $\sin^ {-1}\left (\frac {2} {3}\right)$ will always lie between –? /2 to? /2.

$y={\sin }^{?1}\left(\frac{2}{3}\right)?\sin \left(y\right)=\frac{2}{3}?y?[?\frac{?}{2},\frac{?}{2}]$  

7.33

Xe and F₂ combine under different conditions to produce XeF₂, XeF₄, XeF₆ as follows:

7.66

4NaCl + MnO₂ + 4H₂SO₄ MnCl₂ + 4NaHSO₄ + 2H₂O + Cl₂

Manganese (IV) oxide reacts with sodium chloride and sulfuric acid to produce manganese (II) chloride, chlorine, sodium bisulfate and water.

This reaction takes place at a temperature near 100°C.

Cl₂ + NaI  2NaCl + I₂

Chlorine reacts with sodium iodide to produce sodium chloride and iodine. Chlorine - diluted solution.

Sodium iodide - cold solution.

7.65 

Let the oxidation state of P be x:

7.64 

Neil Bartlett first performed an experiment in which reaction between oxygen and PtF₆ was carried out which lead to the formation of a red coloured compound O₂ ⁺ [PtF₆ ]^-.

He observed that the first ionization energy of Oxygen and Xenon is almost same (~1170 kJ/mol). So, he tried to react Xe and PtF₆ in which he was successful to obtain a red coloured compound Xe⁺ [PtF₆]^-.

7.63

By Deacon's process Cl₂ can be prepared from HCl in presence of CuCl₂

4HCl + O₂? 2Cl₂ + 2H₂O

Cl₂ on treating with water gives HCl

Cl₂ + H₂O? HCl + HOCl