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In theorem 1 of trignometric equations in NCERT textbook class 11 where
 
sin x = sin y
 
I cannot understand after this specific line of the theorem.X equals space left parenthesis 2 n plus 1 right parenthesis straight pi space minus space straight y space space space space space space or space space space space straight X equals space 2 nπ plus space straight y space space space where space straight n element of straight Z
 
Can you please explain how we arrive at the solution  X space equals space n straight pi space plus left parenthesis negative 1 right parenthesis to the power of straight n space end exponent straight y space where space straight n element of straight Z
by completely explaining the steps in between ?
 
 

Asked by Varsneya Srinivas 12th June 2016, 4:33 PM
Answered by Expert
Answer:
begin mathsize 12px style W e space g e t space t w o space c a s e s colon
X space equals space left parenthesis 2 n plus 1 right parenthesis straight pi space minus space straight y space space space space space space or space space space space space space space straight X equals 2 nπ plus straight y

As space you space can space notice comma space in space the space first space case space straight pi space is space multiplied space by space an space odd space number space left parenthesis 2 straight n plus 1 right parenthesis
and space straight y space has space straight a space negative space coefficient.

In space the space second space case comma space straight pi space is space multiplied space by space an space even space number space 2 straight n
and space straight y space has space straight a space positive space coefficient. space

So comma space if space we space want space to space combine space both space the space results space and space write space in space one space form comma
We space use space the space fact space that space open parentheses negative 1 close parentheses to the power of straight n space is space negative space for space apostrophe straight n apostrophe space is space odd space and space positive space for space apostrophe straight n apostrophe space is space even.
So space this space factor space open parentheses negative 1 close parentheses to the power of straight n comma space multiplied space to space apostrophe straight y apostrophe space takes space care space of space both space the space cases. space
When space apostrophe straight n apostrophe space is space odd comma space apostrophe straight y apostrophe space has space straight a space negative space coefficient comma
and space when space apostrophe straight n apostrophe space is space even comma space apostrophe straight y apostrophe space has space straight a space positive space coefficient.

So space we space write space the space result space in space one space form space as space
straight X equals nπ plus open parentheses negative 1 close parentheses to the power of straight n straight y.

Hope space that space clears space your space doubt. end style
Answered by Expert 13th June 2016, 11:37 AM
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