Give solution Share with your friends Share 0 Shruti Tyagi answered this Dear Student, We have an identitity sin-1(x)-sin-1(y)=sin-1x1-y2-y1-x2which can be proved as belowlet sin-1x=a and sin-1y=bhence sina=x and sinb=ythen using formula we get sin(a-b)=sina×cosb-cosa×sinbsin(a-b)=sina×1-sin2b-1-sin2(a)×sinb ---- [using sin2a+cos2a=1, hence cosa=1-sin2a]putting values of sin-1x=a and sin-1y=b, sina=x and sinb=ysin(sin-1x-sin-1y)=x×1-y2-1-x2×ytaking sin-1 on both sidessin-1x-sin-1y=sin-1x×1-y2-1-x2×yHope clears your doubtapplying this formula onsin-112-sin-1x2=sin-112×1-x24-x2×1-14=sin-112×4-x24-x2×4-14=sin-112×2×4-x2-x2×2×3=sin-14-x24-3x4now equate LHS=RHSsin-11-x2=sin-14-x24-3x4⇒1-x2=4-x24-3x44×1-x2=4-x2-3xsquaring both sides161-x2=4-x2+3x2-2×3×4-x2×x16-16x2=4+2x2-2×3×4-x2×x12-18x2=-2×3×4-x2×x6-9x2=3×4-x2×xsquaring both sides36+81x4-108x2=3×4-x2×x236+81x4-108x2=12-3x2×x236+81x4-108x2=12x2-3x436+84x4-120x2=012×7x4-10x2+3=07x4-10x2+3=07x4-7x2-3x2+3=07x2x2-1-3x2-1=0x2-17x2-3=0x2=1 and x2=37x=±1 and x=±37 Regards, -1 View Full Answer
