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Suppose that you are given a system of t...

Suppose that you are given a system of two equations of the following form
`Acosphi=Bv_(1)-Bv_(2)costheta`…………..(1)
`A sinphi=Bv_(2)sin theta`………..(2)
Show that,
`A^(2)=B^(2)(v_(1)^(2)+v_(2)^(2)-2v_(1)v_(2)costheta)`

Text Solution

Verified by Experts

Squaring and adding (1) and (2), we get
`A^(2)(cos^(2)phi+sin^(2)phi)=B^(2)[v_(1)^(2)+v_(2)^(2)(cos^(2)theta+sin^(2)theta)]-v_(1)v_(2)costheta]`
`A^(2)=B^(2)(v_(1)^(2)+v_(2)^(2))(cos^(2)theta+sin^(2)theta)]-v_(1)v_(2)costheta]`
`A^(2)=B^(2)(v_(1)^(2)+v_(2)^(2) - 2v_(1)v_(2)costheta)`
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