Solve equation for t s = 2 ln &#x2061;<!-- ⁡ --> <mrow class="MJX-TeXAtom-ORD">

vrotterigzl

vrotterigzl

Answered question

2022-06-21

Solve equation for t
s = 2 ln | tan ( t ) + sec ( t ) |

Answer & Explanation

benedictazk

benedictazk

Beginner2022-06-22Added 22 answers

A better way to approach the solution:
s = 2 ln | tan ( t ) + sec ( t ) | s 2 = ln | sin ( t ) cos ( t ) + 1 cos ( t ) | e s 2 = | 1 + sin ( t ) cos ( t ) | e s 2 = | [ cos ( t 2 ) + sin ( t 2 ) ] 2 [ cos 2 ( t 2 ) sin 2 ( t 2 ) ] | e s 2 = | [ cos ( t 2 ) + sin ( t 2 ) ] [ cos ( t 2 ) sin ( t 2 ) ] | e s 2 = | [ 1 + tan ( t 2 ) ] [ 1 tan ( t 2 ) ] | e s 2 = tan ( π 4 + t 2 ) t = 2 arctan ( e s 2 ) π 2

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