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  4. If θ=π / 4 n, then the value of tan θ tan 2 θ ⋅s tan (2 n-2) θ tan (2 n-1) θ is

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Q. If $\theta=\pi / 4 n$, then the value of $\tan \theta \tan 2 \theta \cdots \tan (2 n-2)$ $\theta \tan (2 n-1) \theta$ is

Trigonometric Functions

Solution:

$2 n \theta=\pi / 2$. Thus,
$\theta$ and $(2 n-1) \theta=(\pi / 2)-\theta ; 2 \theta$ and $(2 n-2) \theta=(\pi / 2)-2 \theta, \cdots$
form complementary angles $A$ and $B$ so that $\tan A \tan B=\tan A \cot A=1$ for each pair.