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if A+B+C=180 then prove that cos^2a+cos^2b+2cosa*cosb*cosc=sin^2c

if A+B+C=180 then prove that cos^2a+cos^2b+2cosa*cosb*cosc=sin^2c

Grade:11

1 Answers

Lab Bhattacharjee
121 Points
8 years ago
\cos^2A-\sin^2C+2\cos A\cos B\cos C\\ =\cos(A+C)\cos(A-C)+2\cos A\cos B\cos C\\ =\cos(\pi-B)\cos(A-C)+2\cos A\cos B\cos C\\ =\cos B[-\cos(A-C)+2\cos A\cos C]\\ =\cos B[\cos(A+C)]\\ =\cos B[\cos(\pi-B)] \\ =?
 

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