Question

sin(x-y)=?, while sin x + sin y = 2

Answer 1

★ TRIGONOMETRIC REDUCTIONS ★

Sin x + Sin y = 2

Individually , Sin x = 1 and Sin y = 1

Hence , x = 90° , y = 90° ,

Sin ( x - y ) = Sin ( 90° - 90° ) = Sin 0° = 0

★✩★✩★✩★✩★✩★✩★✩★✩★✩★✩★

Answer 2

xsin + ysin = 2
(xsin + ysin)²= 4
x²sin²+y²sin²+2xysin²=4
2xysin²=4-x²sin²-y²sin² — (1)
Now xsin-ysin= √(xsin-ysin)²
=√(x²sin²+y²sin²-2xysin²)
From (1)
√{x²sin²+y²sin²-(4-x²sin²-y²sin²)}
√{x²sin²+y²sin²-4+x²sin²+y²sin²}
√{2x²sin²+2y²sin²-4}
√{2sin²(x²+y²)-4}
√[2{sin²(x²+y²)-2}] Ans.