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## Trigonometric equations **6. ** (1+cosθ)/(1-cosθ) - (1-cosθ)/(1+cosθ) = 4 cotθ cosecθ **7.** (sinθ)/(1+cosθ) + (1+cosθ)/(sinθ) = 2 cosecθ **8.** If cosθ - sinθ = √2 sinθ then prove that cosθ + sinθ = √2 cosθ **9.** If tanθ = n tanφ and sinθ = m sinφ then prove that cos²θ = (m²-1)/(n²-1)...

## Trigonometric equations **6. ** (1+cosθ)/(1-cosθ) - (1-cosθ)/(1+cosθ) = 4 cotθ cosecθ **7.** (sinθ)/(1+cosθ) + (1+cosθ)/(sinθ) = 2 cosecθ **8.** If cosθ - sinθ = √2 sinθ then prove that cosθ + sinθ = √2 cosθ **9.** If tanθ = n tanφ and sinθ = m sinφ then prove that cos²θ = (m²-1)/(n²-1) **10.** If x = a cosecθ and y = b cotθ then prove that (x²/a²) - (y²/b²) = 1 **11.** If x = r sinA cosC, y = r sinA sinC and z = r cosA then prove that r² = x² + y² + z² ## Trigonometric Equations We've learned about trigonometric ratios, and how they relate to each other. Now, let's explore how these relationships can be applied to solve equations. We'll see how trigonometric identities can help us to simplify and solve trigonometric equations, and how to use these equations to solve real-world problems.