Question

find Value of tan(24◦ +θ) – sec(37◦ +θ) – cot (66◦ -θ) + cosec(53◦ -θ) / tan (29◦ +θ) * cot(61◦ -θ)

Answer 1

$$\begin{gathered} \frac{\tan \left(24°+\mathrm{\theta }\right)-\sec \left(37°+\mathrm{\theta }\right)-\cot \left(66°-\mathrm{\theta }\right)+\mathrm{cosec}\left(53°-\mathrm{\theta }\right)}{\tan \left(29°+\mathrm{\theta }\right)\cot \left(61°-\mathrm{\theta }\right)} \\ =\frac{\tan \left[90°-\left(66°-\mathrm{\theta }\right)\right]-\sec \left[90°-\left(53°-\mathrm{\theta }\right)\right]-\cot \left(66°-\mathrm{\theta }\right)+\mathrm{cosec}\left(53°-\mathrm{\theta }\right)}{\tan \left(90°-\left(61°-\mathrm{\theta }\right)\right)\cot \left(61°-\mathrm{\theta }\right)} \\ =\frac{\cot \left(66°-\mathrm{\theta }\right)-\mathrm{cosec}\left(53°-\mathrm{\theta }\right)-\cot \left(66°-\mathrm{\theta }\right)+\mathrm{cosec}\left(53°-\mathrm{\theta }\right)}{\cot \left(61°-\mathrm{\theta }\right)\cot \left(61°-\mathrm{\theta }\right)} \\ =0 \end{gathered}$$