Question

If sec ∞ = 5/4 , then find the value of (1-tan) /(1+tan ∞)

Answer 1

Answer:

1/7

Step-by-step explanation:

sec ∞=5/4

we know ,

sec∞ =h/b =5/4

p=√(5^2-4^2)=3

now, tan∞ =p/b =3/4

so, (1 - tan∞)/(1 +tan∞)

=>(1 -3/4)/(1+3/4)

=>(1/4)/(7/4)=1/7 (answer)

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Answer 2

Given:-

sec∞ =5/4

We have ,

$\tt \sec \infty =\dfrac{h}{b} = \dfrac{5}{4}$

So, perpendicular

$\tt \sqrt {5^{2} - 4^{2}} \\\\ \tt = \sqrt{9} \\\\ \tt =3$

now,

$\tt \tan\infty = \dfrac{p}{b} =\dfrac{3}{4}$

so,

$\dfrac{1 - \tan \infty}{1 +\tan \infty}$

$\tt\Rightarrow \dfrac{(1 -\dfrac{3}{4})}{(1+\dfrac{3}{4})}\\\\ \Rightarrow\tt \dfrac{\dfrac{1}{4}}{\dfrac{7}{4}} \\\\ \Rightarrow \dfrac{1}{7}$