Solution of the differential equation `(dy)/(dx)tany=sin(x+y)+sin(x-y)` is

Options

A. `sec y + 2 cos c = C`
B. ` sec y - 2 cos x = C`
C. ` cos y -2 sin x = C`
D. ` tan y - 2 sec y = C`

Answer

a

Explanation

Given differential equation is
` (dy)/(dx) tan y = sin ( x+y) + sin (x-y)`
` rArr (dy)/(dx) tan y = 2 sin x cos y `
` rArr r = tan y sec y dy = 2 sin x dx `
On integrating both sides , we get
` sec y = -2 cos x + C`
` rArr sec y + 2 cos x = C`