Math, asked by abhiram5399, 9 months ago

Domain of f(x)= the set of all real x for which f(x) is a real number. Find out whether the domains of the following two functions coincide (if they do not then find the common part of the domains of the functions being compared ) y=cosπx and y=cotπx​

Answers

Answered by amitnrw
3

Given : Domain of f(x)= the set of all real x for which f(x) is a real number.  

y=cosπx and y=cotπx​

To find : whether the domains of the following two functions coincide (if they do not then find the common part of the domains of the functions being compared )

Solution:

y=cosπx

cosπx  is defined for all values

Domain of cosπx   is R

y=cotπx​

= cosπx  / Sinπx

y=cotπx​ not defined if Sinπx = 0

Sinπx = 0

=> πx  = nπ  where n ∈ Z

Hence Domain of cotπx​ is R - Z

Domain of cosπx   is R

Domain of cotπx​ is R - Z

Hence domains of two functions does not coincide

the common part of the domains of the functions being compared

R  ∩  (R - Z)

= R - Z

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