Help to simplify arctan &#x2061;<!-- ⁡ --> ( <msqrt>

Micaela Simon

Micaela Simon

Answered question

2022-06-23

Help to simplify arctan ( 1 + x 2 1 x )

Answer & Explanation

sleuteleni7

sleuteleni7

Beginner2022-06-24Added 28 answers

Take x = tan θ So it becomes sec θ 1 t a n θ multiply up and down by cos θ. Becomes 1 c o s θ s i n θ = 2 sin 2 ( θ / 2 ) 2 sin ( θ / 2 ) cos ( θ / 2 ) = tan ( θ / 2 )
So the answer is θ / 2 = ( t a n 1 x ) / 2
crossoverman9b

crossoverman9b

Beginner2022-06-25Added 5 answers

Differentiate with respect to x:
x arctan ( 1 + x 2 1 x ) = 1 x 2 + x 2 + 1 + 1 1 + ( arctan ( 1 + x 2 1 x ) ) 2 = 1 2 ( 1 + x 2 )
Thus:
arctan ( 1 + x 2 1 x ) = 1 2 arctan ( x ) + C
Since both sides are 0 at x=0, then C=0

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?