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A quadrilateral abcd shown in the figure is inscribed in a circle as shown on the figure
the value of cos(A+B+C+D)?
the value of cos(A+B+C+D)?
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A quadrilateral abcd shown in the figure is inscribed in a circle as s...
Quadrilateral Inscribed in a Circle
In a quadrilateral inscribed in a circle, the opposite angles are supplementary. So, we have:
A + C = 180°
B + D = 180°
Sum of Interior Angles
The sum of the interior angles of a quadrilateral is 360°. Therefore, we have:
A + B + C + D = 360°
Expressing in terms of A and B
Substitute the values of A and C in terms of B in the equation A + B + C + D = 360°:
B + B + D + D = 360°
2B + 2D = 360°
B + D = 180°
Cosine of Sum of Angles
The cosine of the sum of angles can be expressed as:
cos(A + B + C + D) = cos(360°) = cos(0°) = 1
Therefore, the value of cos(A + B + C + D) is 1.
In a quadrilateral inscribed in a circle, the opposite angles are supplementary. So, we have:
A + C = 180°
B + D = 180°
Sum of Interior Angles
The sum of the interior angles of a quadrilateral is 360°. Therefore, we have:
A + B + C + D = 360°
Expressing in terms of A and B
Substitute the values of A and C in terms of B in the equation A + B + C + D = 360°:
B + B + D + D = 360°
2B + 2D = 360°
B + D = 180°
Cosine of Sum of Angles
The cosine of the sum of angles can be expressed as:
cos(A + B + C + D) = cos(360°) = cos(0°) = 1
Therefore, the value of cos(A + B + C + D) is 1.
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A quadrilateral abcd shown in the figure is inscribed in a circle as shown on the figurethe value of cos(A+B+C+D)?
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A quadrilateral abcd shown in the figure is inscribed in a circle as shown on the figurethe value of cos(A+B+C+D)? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A quadrilateral abcd shown in the figure is inscribed in a circle as shown on the figurethe value of cos(A+B+C+D)? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A quadrilateral abcd shown in the figure is inscribed in a circle as shown on the figurethe value of cos(A+B+C+D)?.
A quadrilateral abcd shown in the figure is inscribed in a circle as shown on the figurethe value of cos(A+B+C+D)? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A quadrilateral abcd shown in the figure is inscribed in a circle as shown on the figurethe value of cos(A+B+C+D)? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A quadrilateral abcd shown in the figure is inscribed in a circle as shown on the figurethe value of cos(A+B+C+D)?.
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