#09 Reducible to variable separable form | solve differential equation dy/dx=sin(x+y)+cos(x+y)

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Variable Separable Form ,
Solution of first order D.E. by Variable Separable form
solve the differential equation by variable separable form
solve Differential equation dy/dx =sin(x+y)+cos(x+y)
integration of 1/1+sinx+cosx

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Why we convertt 1+tan²z/2 into secz/2
Tanz/2 can simply get cancelled by denominator and the resultant answer will be 1/2
Can i do it ? Pls reply to my query

harmanpreetkaur