Rewrite the expression as a single logarithm and simplify lnabscott+ln(1+tan^2t)

audioblogn8ci

audioblogn8ci

Answered question

2023-02-17

Rewrite the expression as a single logarithm and simplify ln | cot t | + ln ( 1 + tan 2 t )

Answer & Explanation

Reagan Johnston

Reagan Johnston

Beginner2023-02-18Added 4 answers

Use log A B log A + log B
ln | cot t | + ln ( 1 + tan 2 t ) ln ( | cot t | ( 1 + tan 2 t ) )
= ln ( | cot t ( 1 + tan 2 t ) | )
= ln | 1 sin t 1 cos t |
= ln | 1 sin t cos t |
= ln | 2 2 sin t cos t |
= ln | 2 sin ( 2 t ) |
= ln | 2 csc ( 2 t ) |

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