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I) tan v= -1 = tan (- π/4)
Particualr Value, v= -π/4
General Value, v= nπ - π/4, where n=0,1,2,.....
II) tan v= 2 = tan (63.4349...)
Particualr Value, v= tan^-1(2)
General Value, v= nπ +tan^-1(2), where n=0,1,2,.....
III) tan v= 5/2 = tan (68.1986...)
Particualr Value, v= tan^-1(5/2)
General Value, v= nπ +tan^-1(5/2), where n=0,1,2,....
IV) sin x = tan x
sin x cos x - sinx = 0 ( as tan x = sin x/ cos x )
sin x (cos x -1) =0
either sin x = 0 to cos x = 1
in general x = nπ, where n= 0,1,2,....
V) 2sin x = tan x
2 sin x cos x - sinx = 0 ( as tan x = sin x/ cos x )
sin x (2 cos x -1) =0
either sin x = 0 to cos x = 1/2
if sin x = 0, in general x = nπ, where n= 0,1,2,...
if cos x = 1/2, in general x = 2nπ +/- π/3, n= 0,1,2,...
Hence either x = nπ or x = 2nπ +/- π/3, n= 0,1,2,...
Well, I don't understand exactly what u r seeking. But I'm still trying to help you-
let y=x^2
the log y = 2 log x
on differenciating
dy/y = 2 dx/x
Hence the accuracy % of a square root ( x in this particular case) should be 1/2 of the accuracy % of the number (y in this particular case) itself.
And as for these rules (a) and (b) is concern, these can be assumed as basic postulates related with concept of inifinity
Yah, I was expecting this question.
The explanation of value of infinity/ infinity is as following :-
Rule (a) suggests that the value of this fraction should be infinity
and the rule (b) suggests that the value of this fraction should be zero; hence we get a contradiction and the values suggested by numerator and denominator can't be made to agree.
In this case we arise to a conclusion that the value of this fraction
infinity/infinity is indeterminant.
Some other indeterminant forms can be quoted as:
0xinfininy and 0/0
Obiviously the second one fraction quoted above involves a no., i.e. 0, which is very well known to us and none can question its existence and still this fraction 0/0 is indeterminant.
One more thing, these indeterminant forms are very useful in higher maths and a very important L'Hospital Rule for finding limits is applicable only when a fraction is in indeterminant form 0/0 or inifinity/infinity.
Let's consider the problem to findout the value of 1/infinity.
Here the numerator doesnot suggest any specific law to findout the value of the fraction and a fraction, having numerator as 1, can take any possible value whether fininte of infinite,
Now we consider the denominator, i.e., infinity. There are some specific rules to find out value of an expression having infinity as a term:-
a) If infinity appears in the numerator the fraction takes the value infinity
b) If infinity appears in the denominator the fraction takes the value zero.
Here rule (b) about infinty suggests that the value of this fraction 1/inifnity should be zero and the numerator 1 expesses the possibility of this value and there is no contradiction between the result obtained.
Hence the value of 1/inifinity must be zero.
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