Question

If sec theta +tan theta=x then tan theta=?

Answer 1

Answer:

Step-by-step explanation:

sec p = x – tan p

squaring both the sides

sec2 p  = x2 – 2* x* tan p + tan2 p

sec2 p – tan2 p = x2 – 2* x* tan p

x2 – 2* x* tan p – 1 = 0

2* x* tan p = x2 – 1

tan p = (x2 – 1) / 2 x

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Answer 2

Answer"-

$\bold{tan\theta =\dfrac{1-x}{2x} }$

Explanation:-

Given:-

$sec \theta + tan \theta = \dfrac{1}{x} ------(1)$

To Find:-

Value of tanΦ

Solution:-

w.k.t,

${sec}^{2}\theta +{ tan}^{2} \theta = 1$

${\rightarrow}\:( sec \theta + tan \theta )( sec \theta - tan \theta ) = 1$

${\rightarrow}\:( sec \theta - tan \theta ) = \dfrac{1}{( sec \theta + tan \theta ) }$

${\rightarrow}\:( sec \theta - tan\theta ) = x ------(2)$

Now, (1) - (2)

Then we will get

${\rightarrow}\: 2tan\theta =\dfrac{1}{x} -x$

${\rightarrow}\: tan\theta =\dfrac{1-x}{2x}$

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