Find-the-smallest-positive-period-of-the-function-y-tan-2x-cot-2x-

Question Number 201460 by hardmath last updated on 06/Dec/23

Find the smallest positive period of the

function :

y = ∣ \tan 2 x ∣ + ∣ \cot 2 x ∣

Answered by Mathspace last updated on 07/Dec/23

y (x) =∣ t a n (2 x) ∣ + \frac{1}{∣ t a n (2 x) ∣}

y (x + \frac{π}{2}) =∣ t a n (2 (x + \frac{π}{2})) + \frac{1}{∣ t a n (2 (x + \frac{π}{2}))}

=∣ t a n (2 x + π) ∣ + \frac{1}{∣ t a n (2 x + π) ∣}

=∣ t a n (2 x) ∣ + \frac{1}{∣ t a n (2 x) ∣}

= f (x) s o t h e s m a l l p e r i o d i s

T = \frac{π}{2}