Advertisements
Advertisements
Question
यदि F(x) = `[("cos x", "-sin x", 0),("sin x", "cos x", 0),(0,0,1)]` है तो सिद्ध कीजिए कि F(x) · F(y) = F(x + y)
Solution
यहाँ F (x) = `[(cosx, -sinx, 0),(sinx, cosx, 0),(0, 0, 1)]`
∴ F (y) = `[(cosy, -siny, 0),(siny, cosy, 0),(0,0,1)]`
∴ F (x + y) = `[(cos(x+y),-sin(x+y), 0), (sin(x+y),cos(x+y),0),(0,0,1)]`
अब, = F (x). F(y)
= `[(cosx,-sinx,0),(sinx,cosx,0),(0,0,1)][(cosy,-siny,0),(siny,cosy,0),(0,0,1)]`
= `[(cosxcosy-sinxsiny,-cosxsiny-sinxsiny,0),(sinxcosy+cosxsiny,-sinxsiny+cosxcosy,0),(0,0,1)]`
`= [(cos (x + y), -sin (x + y), 0), (sin (x + y), cos (x + y), 0), (0,0,1)]`
APPEARS IN
RELATED QUESTIONS
मान लीजिए कि `A = [(2,4),(3,2)] , B = [(1,3),(-2,5)], C = [(-2,5),(3,4)]`, तो निम्नलिखित ज्ञात कीजिए:
A + B
मान लीजिए कि `"A" = [(2,4),(3,2)], "B" = [(1,3),(-2,5)], "C" = [(-2,5),(3,4)]`, तो निम्नलिखित ज्ञात कीजिए:
A - B
मान लीजिए कि `A = [(2,4),(3,2)] , B = [(1,3),(-2,5)], C = [(-2,5),(3,4)]`, तो निम्नलिखित ज्ञात कीजिए:
3A - C
मान लीजिए कि `A = [(2,4),(3,2)] , B = [(1,3),(-2,5)], C = [(-2,5),(3,4)]`, तो निम्नलिखित ज्ञात कीजिए:
AB
मान लीजिए कि `A = [(2,4),(3,2)] , B = [(1,3),(-2,5)], C = [(-2,5),(3,4)]`, तो निम्नलिखित ज्ञात कीजिए:
BA
