Question

Good morning friends...

Q.what is formula of sinX=sinY?

Answer 1

Hey there !

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sin x= sin y 
sin x-siny =0 
2cos [( x+y)/2] sin [(x-y)/2] 
cos (x+y)/2=0 or sin (x-y)/2=0

general formula

(x+y)/2 = (2n+1)π/2

=> (x-y)/2 =nπ
x+y= (2n+1) π

=> x-y= 2nπ
x= (2n+1) π+ x= 2nπ + y

therefore final general solution

x= nπ + (-1)raised to n y, where n €z

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Hope it helps you !

by : Sami91

Answer 2

we have to findsin X =sinY=_________

sinX - sinY =0
cos [( (X+Y )/2 ) sin( (X-Y)/2)]
cos(X+Y)=0 or cos ( X- Y )=0
WKT
X+Y/2 =2n +1 /π2
X+Y=(2n+1)π and. X-Y =2nπ
X=( 2n +1)n ;. X=2nπ + Y
.•.general solution X=nπ -1 n value can be changed y
n€ Z