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Find the principal and general solutions of the following equations: cot x = -√3
Solution:
It is given that cot x = -√3
We know that cot is negative in the second and the fourth quadrants.
We know that cot π/6 = √3.
In the second quadrant, x = π - π/6 = 5π/6 as cot 5π/6 = cot (π - π/6) = -cot π/6 = -√3
In the fourth quadrant, x = 2π - π/6 = 11π/6 as cot 11π/6 = cot (2π - π/6) = -cot π/6 = -√3
Thus, the principle solutions are: x = 5π/6, and 11π/6.
Now,
cot x = cot 5π/6
tan x = tan 5π/6
Therefore, x = nπ + 5π/6, where n∈Z is the general solution.
NCERT Solutions Class 11 Maths Chapter 3 Exercise 3.4 Question 3
Find the principal and general solutions of the following equations: cot x = -√3
Summary:
The principal solutions are x = 5π/6 and 11π/6 and the general solution is x = nπ + 5π/6, where n∈Z.
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