Prove the following: cos(sin⁻¹(3/5) + cot⁻¹(1)) = 65√13

cos(sin⁻¹(3/5) + cot⁻¹(1)) = cos(sin⁻¹(3/5))cos(cot⁻¹(1)) - sin(sin⁻¹(3/5))sin(cot⁻¹(1))
Let sin⁻¹(3/5) = θ. Then sin θ = 3/5. We can construct a right-angled triangle with opposite side 3 and hypotenuse 5. The adjacent side is √(5² - 3²) = 4. Therefore, cos θ = 4/5.
Let cot⁻¹(1) = φ. Then cot φ = 1, which means tan φ = 1. This implies φ = π/4. Thus, cos φ = √2/2 and sin φ = √2/2.
Substituting these values into the equation:
cos(sin⁻¹(3/5) + cot⁻¹(1)) = (4/5)(√2/2) - (3/5)(√2/2) = (4√2 - 3√2)/10 = √2/10
However, the given solution is incorrect. Let's reconsider the problem and solution provided. There seems to be a mistake in the given solution. The given equation to prove cos(sin⁻¹(3/5) + cot⁻¹(1)) = 65√13 is likely incorrect.