Show that the triangle is a right triangle

AI Thread Summary
To demonstrate that the triangle is a right triangle, start by manipulating the equations sin(A+B) = 1/sin(C) and cos(A+B) = cos(C) to express A+B in terms of C. By applying the sine and cosine addition formulas, you can derive relationships between the angles. Solving these equations will reveal the value of C, which leads to determining angles A and B. The resulting calculations confirm that one of the angles must be 90 degrees, establishing that the triangle is indeed a right triangle. This approach effectively utilizes compound angle formulas to arrive at the conclusion.
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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.
 
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You need to show your work. But for starters, one way that you can approach this problem is to solve for "A+B" in both equations in terms of "C". Then you can solve for "C" using these two equations. Last, solve for A and B.
 
Yeah, compound angle formulae a-gogo!
 

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