Question 138
a)
Verify that $(1+\tan k)\left(1+\tan\left(45^\circ-k\right)\right)=2$.
b)
Given that
$$
\left(1+\tan 1^\circ\right)\left(1+\tan 2^\circ\right) \cdot \ldots \cdot\left(1+\tan 45^\circ\right)=2^n
$$
find $n$.
Verify that $(1+\tan k)\left(1+\tan\left(45^\circ-k\right)\right)=2$.
b)
Given that
$$
\left(1+\tan 1^\circ\right)\left(1+\tan 2^\circ\right) \cdot \ldots \cdot\left(1+\tan 45^\circ\right)=2^n
$$
find $n$.