Question

Solve tan 1° + tan89° =​

Answer 1

Step-by-step explanation:

tan(1°) + tan(89°) = tan(1°) + cot(1°)

$= \frac{sin {1}^{o} }{cos {1}^{o} } + \frac{cos {1}^{o} }{sin {1}^{o} } = \frac{sin {}^{2} {1}^{o} + cos {}^{2} {1}^{o} }{sin {1}^{o}cos {1}^{o} } = \frac{1}{sin {1}^{o} + cos {1}^{o} }$

$= \frac{2}{2 \: sin {1}^{o \: }cos {1}^{o} } = \frac{2}{sin \: 2 {}^{o} }$

Formula used: sin²θ + cos²θ = 1 and sin2θ = 2sinθcosθ

Also cot(90° − θ) = cotθ