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प्रश्न
Prove the following :
`(sin2x + sin2y)/(sin2x - sin2y) = (tan(x + y))/(tan(x - y))`
उत्तर
L.H.S. = `(sin2x + sin2y)/(sin2x - sin2y)`
= `(2sin ((2x + 2y)/2)cos((2x - 2y)/2))/(2cos((2x + 2y)/2)sin((2x - 2y)/2)`
= `(sin(x + y)cos(x - y))/(cos(x + y)sin(x - y))`
= tan (x + y) . cot (x – y)
= `tan(x + y)*1/(tan(x - y)`
= `(tan(x+ y))/(tan(x - y))`
= R.H.S.
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