for the question dy/dx = sin (x+y) how these steps come I need step by step explanation
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It is simple first they have swapped the denominator and the they have multiplied with (1-sinz) in both the numerator and denominator
since
(a^2-b^2)=(a-b)(a+b)
therefore
(1-sinz)*(1+sinz) = (1^2-(sin^2)z)
Now
since (sin^2)x+(cos^2)x=1
Therefore
(cos^2)x=1-(sin^2)x
now substituting this value of 1-(sin^2)x in the denominator and then seperate the individual terms like
(1/(cos^2)x)-(sinz/(cos^2)x)
now
since 1/cosx= secx
and
sinx/cosx = tanx
we get those values and finally integrate the whole equation.
since
(a^2-b^2)=(a-b)(a+b)
therefore
(1-sinz)*(1+sinz) = (1^2-(sin^2)z)
Now
since (sin^2)x+(cos^2)x=1
Therefore
(cos^2)x=1-(sin^2)x
now substituting this value of 1-(sin^2)x in the denominator and then seperate the individual terms like
(1/(cos^2)x)-(sinz/(cos^2)x)
now
since 1/cosx= secx
and
sinx/cosx = tanx
we get those values and finally integrate the whole equation.
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