Question

$\frac{2}{3}{\text{cosec}}^2{58}^0-\frac{2}{3}\cot {58}^0\tan {32}^0-\frac{5}{3}\tan {13}^0\tan {37}^0\tan {45}^0\tan {53}^0\tan {77}^0=-m$.Find $m$

Answer 1

$\frac{2}{3}cose{c}^{2}58°-\frac{2}{3}\cot 58°.\tan 32°-\frac{5}{3}\tan 13°.\tan 37°.\tan 45°.\tan 53°.\tan 77°$

$⟹\frac{2}{3}cose{c}^{2}58°-\frac{2}{3}{\cot }^{2}58°-\frac{5}{3}=\frac{2}{3}(cose{c}^{2}58°-{\tan }^{2}58°)-\frac{5}{3}$

$⟹\frac{2}{3}-\frac{5}{3}=\frac{2-5}{3}=\frac{-3}{3}=-1$