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Prove that: s in^2A=cos^2(A-B)+cos^2B-2c...

Prove that: `s in^2A=cos^2(A-B)+cos^2B-2cos(A-B)cosAcosBdot`

Text Solution

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RHS`=cos^(2)(A-B)-2cos(A-B)cosAcosB+cos^(2)B`
`=cos(A-B)(cosAcosB+sinAsinB-2cosAcosB)+cos^(2)B`
`-cos(A-B)(cosAcosB-sinAsinB)-2cosAcosB)+cos^(2)B`
`=-cos(A-B)(cosAcosB-sinAsinB)+cos^(2)B`
`-cos(A-B)cos(A+B)+cos^(2)B`
`-(cos^(2)A-sin^(2)B)+cos^(2)B`
`-cos^(2_)A+1=sin^(2)A`= LHS Hence Proved.
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