What is the tangent of 2sec(x) ?

The tangent of 2sec(x) is y=2sec(a_{0})tan(a_{0})x+2sec(a_{0})-2sec(a_{0})tan(a_{0})a_{0}

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tangent of 2sec(x)

tangent of

2 sec (x)

y = 2 sec (a_{0}) tan (a_{0}) x + 2 sec (a_{0}) - 2 sec (a_{0}) tan (a_{0}) a_{0}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, 2 sec (a_{0}))

Find the slope of

y = 2 sec (x) : \frac{d y}{d x} = 2 sec (x) tan (x)

EN : T i tl e G e n er a l Eq u a t i o n Sl o p e A t P o in t 2 Eq : m = 2 sec (a_{0}) tan (a_{0})

Find the line with slope m=

2 sec (a_{0}) tan (a_{0})

and passing through

(a_{0}, 2 sec (a_{0})) : y = 2 sec (a_{0}) tan (a_{0}) x + 2 sec (a_{0}) - 2 sec (a_{0}) tan (a_{0}) a_{0}

y = 2 sec (a_{0}) tan (a_{0}) x + 2 sec (a_{0}) - 2 sec (a_{0}) tan (a_{0}) a_{0}

What is the tangent of 2sec(x) ?
The tangent of 2sec(x) is y=2sec(a_{0})tan(a_{0})x+2sec(a_{0})-2sec(a_{0})tan(a_{0})a_{0}