Question

Sin( 1+ tan)+cos(1+cot)=sec+cosec​

Answer 1

$sin(1 + tan) + cos(1 + cot) \\ = sin( \frac{cos + sin}{cos} ) + cos( \frac{cos + sin}{sin} ) \\ = (cos + sin)( \frac{sin}{cos} + \frac{cos}{sin} ) \\ = (cos + sin)( \frac{ {sin}^{2} + {cos}^{2} }{sin \: cos} ) \\ = \frac{cos + sin}{sin \: cos} \\ = \frac{1}{sin} + \frac{1}{cos} \\ = cosec + sec$