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If ABCD is a cyclic quadrilateral then the value of cos^2A-cos^2B-cos^2C+cos^2D

If ABCD is a cyclic quadrilateral then the value of cos^2A-cos^2B-cos^2C+cos^2D

Grade:10

1 Answers

Aditya srinivas
52 Points
7 years ago
The main concept involving is that in a cyclic quadrilateral the sum of opposite angles is equal to 180 degrees. Then consider Cos^2A-cos^2c and cos^2D-cos^2B and apple the formula a^2-b^2 = [a+b]*[a-b] And next apply the cosA-cosB formula and cosA+cosB formula for both the terms and convert it by applying sin2A formula. Then we get sine in terms of A+B and A-B. Since we knew that A+C and B+D is equal to 180 degrees then replace A+c by 180 and B+D by 180 hence we get the answer as 0.

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