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prove the following

Q(22) \small \cot x \cot2x - \cot2x\cot3x - \cot3x\cot x =1

Q(23) Prove that

 \small \tan4x = \frac{4\tan x(1-\tan^{2}x)}{1-6 \tan^{2}x+\tan^{4}x}

Q(24) Prove the following 

\small \cos4x = 1 - 8\sin^{2}x\cos^{2}x

Q(25)  Prove the following

\small \cos6x = 32\cos^{6}x -48\cos^{4}x + 18\cos^{2}x-1

9.1 Justify the position of hydrogen in the periodic table on the basis of its electronic configuration

9.2  Write the names of isotopes of hydrogen. What is the mass ratio of these isotopes ?

9.3 Why does hydrogen occur in a diatomic form rather than in a monoatomic form under normal conditions ?

9.4 How can the production of dihydrogen, obtained from ‘coal gasification’, be increased?

9.5  Describe the bulk preparation of dihydrogen by an electrolytic method. What is the role of an electrolyte in this process?

9.6 Complete the following reactions

\\(i)H_{2}(g)+MmOo(s)\rightarrow \\ (ii)CO(g)+H_{2}(g)\rightarrow \\ (iii)C_{3}H_{8}(g)+3H_{2}O(g)\rightarrow\\ (iv)Zn(s)+NaOH(aq)\rightarrow

9.7  Discuss the consequences of high enthalpy of H–H bond in terms of chemical reactivity of dihydrogen?

9.8  What do you understand by (i) electron-deficient, (ii) electron-precise, and (iii) electron-rich compounds of hydrogen? Provide justification with suitable examples.

9.9  What characteristics do you expect from an electron-deficient hydride with respect to its structure and chemical reactions

9.1o  Do you expect the carbon hydrides of the type (CnH2n + 2) to act as ‘Lewis’ acid or base? Justify your answer. 

9.11  What do you understand by the term “non-stoichiometric hydrides”? Do you expect this type of the hydrides to be formed by alkali metals? Justify your answer

9.12  How do you expect the metallic hydrides to be useful for hydrogen storage? Explain

9.13  How does the atomic hydrogen or oxy-hydrogen torch function for cutting and welding purposes? Explain. 

9.14 Among NH3, H2O and HF, which would you expect to have highest magnitude of hydrogen bonding and why?

Saline hydrides are known to react with water violently producing fire Can CO2 a well known fire extinguisher be used in this case? Explain

9.16  Arrange the following

(i) CaH2, BeH2 and TiH2 in order of increasing electrical conductance

9.16 Arrange the following

(ii) LiH, NaH and CsH in order of increasing ionic character

9.16 arrange the following 

(iii) H–H, D–D and F–F in order of increasing bond dissociation enthalpy

Arrange the following  NaH, MgH_2, and H_2O in order of increasing reducing property

9.17  Compare the structures of H2O and H2O2.

9.18 What do you understand by the term auto-protolysis of water? What is its significance?

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