Say I want to solve this equation using product cancellation: cos &#x2061;<!-- ⁡ --> ( 2

Sonia Gay

Sonia Gay

Answered question

2022-06-16

Say I want to solve this equation using product cancellation:
cos ( 2 x + π 2 ) tan 3 x = 0

Answer & Explanation

Braylon Perez

Braylon Perez

Beginner2022-06-17Added 34 answers

The problem is that while
lim x π 2 [ cos ( 2 x + π 2 ) ] = 0
is true,
lim x π 2 [ tan ( 3 x ) ] =
so we cannot not just say that the product is equal to zero. We can take the limit of the product,
lim x π 2 [ cos ( 2 x + π 2 ) tan ( 3 x ) ] = 2 3 0
Thus only π 3 k works.

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