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bbanbury
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If angles A, B, and C are the angles of a triangle such that sin(A+B)=1/sin(C) and cos(A+B)=cos(C), then show that the triangle is a right triangle.
Show that the triangle is a right triangle
- Thread starter bbanbury
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SUMMARY
The discussion focuses on proving that a triangle is a right triangle given the equations sin(A+B) = 1/sin(C) and cos(A+B) = cos(C). By manipulating these equations, one can express A+B in terms of C and subsequently derive the values of angles A and B. The use of compound angle formulas is essential in this proof, leading to the conclusion that if these conditions hold, angle C must be 90 degrees, confirming the triangle's right-angle status.
PREREQUISITES- Understanding of trigonometric identities and equations
- Familiarity with compound angle formulas
- Basic knowledge of triangle properties and angle relationships
- Ability to manipulate algebraic equations
- Study trigonometric identities, particularly the sine and cosine functions
- Learn about compound angle formulas in trigonometry
- Explore properties of right triangles and the Pythagorean theorem
- Practice solving trigonometric equations and angle relationships in triangles
Students studying geometry, mathematics educators, and anyone interested in understanding trigonometric proofs related to triangle properties.
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