Question

The value of tan380 + cot20 is​

Answer 1

Answer:

$tan \: 380 \degree + cot \: 20 \degree \\ = tan \: (360\degree +20\degree) + cot \: 20 \degree \\ ..( \because \:tan \: (360\degree +\theta) = tan \theta) \\ = tan \: 20 \degree + cot \: 20 \degree \\ </p><p>=\frac{sin\: 20\degree}{cos\: 20\degree} +\frac{cos\: 20\degree}{sin\: 20\degree} \\</p><p>=\frac{sin\: 20\degree\times sin\: 20\degree}{cos\: 20\degree\times sin\: 20\degree} +\frac{cos\: 20\degree\times cos\: 20\degree}{sin\: 20\degree\times cos\: 20} \\</p><p>=\frac{sin^2 \: 20\degree}{cos\: 20\degree\times sin\: 20\degree} +\frac{cos^2\: 20\degree}{sin\: 20\degree\times cos\: 20\degree} \\</p><p>=\frac{sin^2 \: 20\degree+cos^2 \: 20\degree}{cos\: 20\degree\times sin\: 20\degree}\\ </p><p>=\frac{1}{cos\: 20\degree\times sin\: 20\degree}\\ </p><p>=\frac{1}{cos\: 20\degree}\times\frac{1}{sin\: 20\degree} \\</p><p>= sec\: 20\degree\times cosec\: 20\degree\\</p><p>= sec\: 20\degree\:cosec\: 20\degree</p><p>$