यदि `theta-phi=(pi)/(2)`, तो सिद्ध कीजिए कि - `[{:(cos^(2)theta,costhetasintheta),(costhetasintheta,sin^(2)theta):}][{:(cos^(2)phi,cosphisinphi),(cosp

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यदि `theta-phi=(pi)/(2)`, तो सिद्ध कीजिए कि - `[{:(cos^(2)theta,costhetasintheta),(costhetasintheta,sin^(2)theta):}][{:(cos^(2)phi,cosphisinphi),(cosp

यदि `theta-phi=(pi)/(2)`, तो सिद्ध कीजिए कि -
`[{:(cos^(2)theta,costhetasintheta),(costhetasintheta,sin^(2)theta):}][{:(cos^(2)phi,cosphisinphi),(cosphisinphi,sin^(2)phi):}]=O`.

Monjur Alahi

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2025-01-04 04:42

1 Answers

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

`L.H.S=[{:(cos^(2)theta,costhetasintheta),(costhetasintheta,sin^(2)theta):}]`
`[{:(cos^(2)phi,cosphisinphi),(costhetasintheta,sin^(2)phi):}]`
`=[{:(cos^(2)thetacos^(2)phi+costhetacosphisinthetasinphi,cos^(2)thetacosphisinphi+costhetasinthetasin^(2)phi),(costhetacos^(2)phisintheta+sin^(2)thetacosphisinphi,costhetasinthetacosphisinphi+sin^(2)thetasin^(2)phi):}]`
`=[{:(costhetacosphi(costhetacosphi+sinthetasintheta),costhetasinphi(costhetacosphi=sinthetasinphi)),(cosphisintheta(costhetacosphi+sinthetasinphi),sinthetasinphi(costhetacosphi+sinthetasinphi)):}]`
`=[{:(costhetacosphi*cos(theta-phi),costhetasinphicos(theta-phi)),(cosphisintheta*cos(theta-phi),sintheta sinphicos(theta-phi)):}]`
`=[{:(costhetacosphi*cospi//2,costhetasinphi*cospi//2),(cosphisintheta*cospi//2,sinthetasinphi*cospi//2):}]`
`=[{:(0,0),(0,0):}]=O=R.H.S`. यही सिद्ध करना था ।