Q55 of 303 Page 4

Answer each of the following questions in one word or one sentence or as per exact requirement of the question:

Write the value of , when .


Given


We know that tan-1 x + cot-1 x = π/2


= cos (π/6)


= √3/2


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53

Answer each of the following questions in one word or one sentence or as per exact requirement of the question:

Write the value of for x < 0 in terms of cot–1(x).


 54

Answer each of the following questions in one word or one sentence or as per exact requirement of the question:

Write the value of cot–1(–x) for all x ∈ R in terms of cot–1x.


 56

Answer each of the following questions in one word or one sentence or as per exact requirement of the question:

If , find the value of x.


 57

Answer each of the following questions in one word or one sentence or as per exact requirement of the question:

Find the value of .