The discussion focuses on solving the trigonometric identity \(\frac{2-5\cot(x)}{2+5\cot(x)}=\frac{2\sin(x)-5\cos(x)}{2\sin(x)+5\cos(x)}\). Participants confirm the identity's correctness and suggest two methods for simplification: multiplying the left side by \(\frac{\sin x}{\sin x}\) or the right side by \(\frac{\csc x}{\csc x}\). Additionally, they clarify the definitions of cotangent and cosecant, stating that \(\cot x = \frac{\cos x}{\sin x}\) and \(\csc x = \frac{1}{\sin x}\).
PREREQUISITESStudents, educators, and anyone looking to enhance their understanding of trigonometric identities and algebraic manipulation in trigonometry.
fluffertoes said:How do you do this one? I can't figure it out!
(2 - 5cot x) / (2 + 5cot x) = (2sin x - 5cos x) / (2sin x + 5cos x)