An equation to the tangent line of h ( x ) = tan &#x2061;<!-- ⁡ --> ( x

Jamir Melendez

Jamir Melendez

Answered question

2022-05-09

An equation to the tangent line of h ( x ) = tan ( x ) + cos ( x ) is given by y = m x + b where m is the slope and b is the y-intercept. If x = π 4 find m.

Answer & Explanation

Duncan Cox

Duncan Cox

Beginner2022-05-10Added 18 answers

If
(1) h ( x ) = tan x + cos x ,
then
(2) h ( x ) = sec 2 x sin x = 1 / ( cos 2 x ) sin x ,
so if x = π / 4
(3) m = h ( π / 4 ) = 2 2 / 2.

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