The value of cotθ.tan(90° - θ) - sec(90° - θ)cosecθ + (sin225° + sin265°) + 3 (tan5°. tan15°. tan30°. tan75°. tan85°)

Answer: Option A

cotθ. tan(90° - θ) - sec(90° - θ)cosecθ + (sin²25° + sin²65°) + $$\sqrt{3}$$ (tan5°. tan15°. tan30°. tan75°. tan85°)
= cotθ. cotθ - cosecθ. cosecθ + (sin²25° + cos²25° ) + $$\sqrt{3}$$ [(tan5°. tan85°) . (tan15°. tan75°). tan30°]
  $$=\left(\text{co}{\text{t}}^2\theta -\text{cose}{\text{c}}^2\theta \right)+\left(1\right)+\sqrt{3}\left(\mathrm{1.1.}\frac{1}{\sqrt{3}}\right)$$         $$\left[\text{tan A}\text{.tan B}=\text{1, If A}+\text{B}={90}^{\circ }\right]$$
$$\begin{array}{rl}& =\left(-1\right)+\left(1\right)+\sqrt{3}\times \frac{1}{\sqrt{3}}\\ & =-1+1+1\\ & =1\end{array}$$