Show that the triangle is a right triangle

[bbanbury]

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.

 

[konthelion]

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.

 

[Chewy0087]

Yeah, compound angle formulae a-gogo!