Find the value of cos &#x2061;<!-- ⁡ --> tan <mrow class="MJX-TeXAtom-ORD">

Damon Stokes

Damon Stokes

Answered question

2022-06-21

Find the value of cos tan 1 sin cot 1 ( x )
... Let cot 1 x = z
x = cot z
Then,
sin cot 1 ( x )
= sin z
= 1 csc z
= 1 1 + cot 2 z
= 1 1 + x 2

Answer & Explanation

Josie123

Josie123

Beginner2022-06-22Added 16 answers

Then we have
cos ( ( tan 1 1 1 + x 2 ) )
If tan 1 1 1 + x 2 = y , π 4 y π 2 tan y = 1 1 + x 2 and cos y 0
cos ( tan 1 1 1 + x 2 ) = cos y = + 1 1 + tan 2 y = ?
Manteo2h

Manteo2h

Beginner2022-06-23Added 4 answers

Let y = 1 1 + x 2 and let tan 1 y = w
Then,
  cos tan 1 y = cos w   Now since  1 y > 0  we have  cos w > 0   = 1 sec w   = 1 1 + tan 2 w   = 1 1 + y 2  
And then substitute y.

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